let H1,H2 be characteristic subgroupsof a given group G=H1×H2 ٰthen K(H1×H2)=K(H1)×K(H2) please give with gap i need
On 1/9/11, zahra sheikhaleslami <zahra.sheikhalesl...@gmail.com> wrote: > hi > please write this theorem with gap > > if G,H are finite groups with (IGI,IHI)=1then > Aut(G×H)=Aut(G)×Aut(H) > > On 1/9/11, forum-requ...@gap-system.org <forum-requ...@gap-system.org> > wrote: >> Send Forum mailing list submissions to >> forum@mail.gap-system.org >> >> To subscribe or unsubscribe via the World Wide Web, visit >> http://mail.gap-system.org/mailman/listinfo/forum >> or, via email, send a message with subject or body 'help' to >> forum-requ...@mail.gap-system.org >> >> You can reach the person managing the list at >> forum-ow...@mail.gap-system.org >> >> When replying, please edit your Subject line so it is more specific >> than "Re: Contents of Forum digest..." >> >> >> Today's Topics: >> >> 1. Help (Sara Radfar) >> 2. Re: Help (Vipul Naik) >> 3. Re: Help (Dr. Ashish Kumar Das) >> 4. First Announcement:Workshop on "Finite Groups & Their >> Automorphisms" in Istanbul (Gulin Ercan) >> 5. Re: Interface with other languages (Alexander Konovalov) >> 6. The Add function (Hebert P?rez-Ros?s) >> 7. Re: The Add function (Keshav Rao Kini) >> 8. Re: The Add function (Hebert P?rez-Ros?s) >> 9. Question (Sara Radfar) >> >> >> ---------------------------------------------------------------------- >> >> Message: 1 >> Date: Thu, 6 Jan 2011 05:14:32 -0800 >> From: Sara Radfar <sararadfa...@gmail.com> >> To: forum <fo...@gap-system.org> >> Subject: [GAP Forum] Help >> Message-ID: >> <aanlktikj7bgyaba0kauiu_vxoc9jao2s3kumrr_xb...@mail.gmail.com> >> Content-Type: text/plain; charset=ISO-8859-1 >> >> Hi >> >> I can find the same order elements of a group but can't find the set >> of the number of the same order elements of a group.Also how we can >> introduce a sporadic simple group to GAP?.For example $CO$. >> >> Thanks >> Sara >> >> >> >> ------------------------------ >> >> Message: 2 >> Date: Thu, 6 Jan 2011 20:22:04 -0600 >> From: Vipul Naik <vi...@math.uchicago.edu> >> To: Sara Radfar <sararadfa...@gmail.com> >> Cc: forum <fo...@gap-system.org> >> Subject: Re: [GAP Forum] Help >> Message-ID: <20110107022204.ga16...@math.uchicago.edu> >> Content-Type: text/plain; charset=us-ascii >> >> Hi, >> >> If I understand your question correctly, you want information on how >> many elements of a finite group have each possible order. Although I >> don't think there are built-in functions for this, it is easy to write >> code for these. For instance: >> >> OrderStatisticsPaired := function(G) >> local L,D; >> L := List(Set(G),Order); >> D := DivisorsInt(Order(G)); >> return(List(D,x->[x,Length(Filtered(L,y->x=y))])); >> end;; >> >> This function takes as input a group and gives a list of ordered >> pairs, for each divisor of the order of the group, how many elements >> of the group have that order. For instance: >> >> OrderStatisticsPaired(SymmetricGroup(4)) >> >> gives the output: >> >> [ [ 1, 1 ], [ 2, 9 ], [ 3, 8 ], [ 4, 6 ], [ 6, 0 ], [ 8, 0 ], [ 12, 0 ], >> [ >> 24, 0 ] ] >> >> indicating that in the symmetric group on four letters, there is one >> element of the group of order one, nine elements of order two, eight >> elements of order three, six elements of order four, and no element of >> any higher order. >> >> This exact function may not suit your needs but it's likely that some >> variant of it will. >> >> This code is inefficient for large groups; for such groups, one can >> modify the code to only go over conjugacy classes instead of elements. >> >> To create such a function, you can either paste the function code in >> front of the GAP command prompt or include this in a file and then use >> GAP's "Read" command to read that file in. >> >> Vipul >> >> * Quoting Sara Radfar who at 2011-01-06 05:14:32+0000 (Thu) wrote >>> Hi >>> >>> I can find the same order elements of a group but can't find the set >>> of the number of the same order elements of a group.Also how we can >>> introduce a sporadic simple group to GAP?.For example $CO$. >>> >>> Thanks >>> Sara >>> >>> _______________________________________________ >>> Forum mailing list >>> Forum@mail.gap-system.org >>> http://mail.gap-system.org/mailman/listinfo/forum >> >> >> >> ------------------------------ >> >> Message: 3 >> Date: Fri, 7 Jan 2011 10:02:53 +0530 >> From: "Dr. Ashish Kumar Das" <akdasn...@gmail.com> >> To: Vipul Naik <vi...@math.uchicago.edu> >> Cc: Sara Radfar <sararadfa...@gmail.com>, forum <fo...@gap-system.org> >> Subject: Re: [GAP Forum] Help >> Message-ID: >> <aanlktim7kgwxe11z7qdgymtwpoxjs9yifonuw1rmw...@mail.gmail.com> >> Content-Type: text/plain; charset=ISO-8859-1 >> >> Hi, >> How about running the following program: >> >> >> n:=90; # try with other values >> i:=0; >> Print("GROUP ORDER is ", " ", n, "\n"); >> g:= AllSmallGroups(n); >> for xx in g do >> i:=i+1; >> Print( "\n", "SMALL GROUP", "(" , n, "," , i, ") = >> ",StructureDescription(xx), "\n","\n"); >> yy:= Set(List(xx,Order)); >> for y in yy do >> zz:= Number(xx, x -> Order(x)=y); >> Print("order = ", y, " ", "number of elts = ", zz, "\n", "\n"); od; >> od; >> >> Ashish Kumar Das >> Maths Dept. >> NEHU, Shillong, INDIA >> >> On 1/7/11, Vipul Naik <vi...@math.uchicago.edu> wrote: >>> Hi, >>> >>> If I understand your question correctly, you want information on how >>> many elements of a finite group have each possible order. Although I >>> don't think there are built-in functions for this, it is easy to write >>> code for these. For instance: >>> >>> OrderStatisticsPaired := function(G) >>> local L,D; >>> L := List(Set(G),Order); >>> D := DivisorsInt(Order(G)); >>> return(List(D,x->[x,Length(Filtered(L,y->x=y))])); >>> end;; >>> >>> This function takes as input a group and gives a list of ordered >>> pairs, for each divisor of the order of the group, how many elements >>> of the group have that order. For instance: >>> >>> OrderStatisticsPaired(SymmetricGroup(4)) >>> >>> gives the output: >>> >>> [ [ 1, 1 ], [ 2, 9 ], [ 3, 8 ], [ 4, 6 ], [ 6, 0 ], [ 8, 0 ], [ 12, 0 ], >>> [ >>> 24, 0 ] ] >>> >>> indicating that in the symmetric group on four letters, there is one >>> element of the group of order one, nine elements of order two, eight >>> elements of order three, six elements of order four, and no element of >>> any higher order. >>> >>> This exact function may not suit your needs but it's likely that some >>> variant of it will. >>> >>> This code is inefficient for large groups; for such groups, one can >>> modify the code to only go over conjugacy classes instead of elements. >>> >>> To create such a function, you can either paste the function code in >>> front of the GAP command prompt or include this in a file and then use >>> GAP's "Read" command to read that file in. >>> >>> Vipul >>> >>> * Quoting Sara Radfar who at 2011-01-06 05:14:32+0000 (Thu) wrote >>>> Hi >>>> >>>> I can find the same order elements of a group but can't find the set >>>> of the number of the same order elements of a group.Also how we can >>>> introduce a sporadic simple group to GAP?.For example $CO$. >>>> >>>> Thanks >>>> Sara >>>> >>>> _______________________________________________ >>>> Forum mailing list >>>> Forum@mail.gap-system.org >>>> http://mail.gap-system.org/mailman/listinfo/forum >>> >>> _______________________________________________ >>> Forum mailing list >>> Forum@mail.gap-system.org >>> http://mail.gap-system.org/mailman/listinfo/forum >>> >> >> >> >> ------------------------------ >> >> Message: 4 >> Date: Fri, 07 Jan 2011 11:25:42 +0200 >> From: Gulin Ercan <er...@metu.edu.tr> >> To: fo...@gap-system.org >> Subject: [GAP Forum] First Announcement:Workshop on "Finite Groups & >> Their Automorphisms" in Istanbul >> Message-ID: <20110107112542.104653muq7sbz...@horde.metu.edu.tr> >> Content-Type: text/plain; charset=ISO-8859-9; DelSp="Yes"; >> format="flowed" >> >> Dear All, >> >> We would like to announce herewith a five-day workshop on "Finite >> groups and their automorphisms" >> which will take place in Istanbul at Bo?azi?i University on 7-11 June >> 2011. >> >> It aims to bring together leading mathematicians and active >> researchers working on >> the theory of groups in order to exchange ideas, present new results and >> identify the key problems in the field. >> >> The workshop is especially interested in and motivated by the >> questions on the relationship >> between a finite group and another one acted upon by the first, >> although it is not to be considered the exclusive theme. >> >> There will be seven mini-courses and some invited talks. >> The speakers who have kindly accepted our invitation to give (a short >> series of)lectures are: >> >> Alan Camina, Martin I.Isaacs, Evgeny Khukhro, Charles Leedham-Green, >> Attila Maroti, Nadia Mazza, Akos Seress, Aner Shalev and Said N.Sidki >> >> There will be a limited number of slots available in the schedule for >> contributed talks as well >> and a poster session. >> >> For details and registration please visit the workshop webpage >> http://www.istanbulgroup.metu.edu.tr >> >> We are looking forward to seeing you in Istanbul!! >> >> >> >> >> >> >> ---------------------------------------------------------------- >> This message was sent using IMP, the Internet Messaging Program. >> >> >> >> >> ------------------------------ >> >> Message: 5 >> Date: Fri, 7 Jan 2011 15:58:05 +0000 >> From: Alexander Konovalov <alexander.konova...@gmail.com> >> To: b...@mat.ug.edu.pl >> Cc: fo...@gap-system.org >> Subject: Re: [GAP Forum] Interface with other languages >> Message-ID: <1d984673-c91c-4f6b-b493-d1843c9e5...@gmail.com> >> Content-Type: text/plain; charset=us-ascii >> >> Dear Bartosz, dear GAP Forum, >> >> There are already several GAP packages that contain C parts and >> use LoadDynamicModule to load them, so probably to begin with >> you may have a look at them. In no particular order, these packages >> are: orb, linboxing, io, HAP, Gauss, FR, EDIM and Browse. >> >> Best wishes, >> Alexander >> >> >> On 10 Dec 2010, at 14:44, b...@mat.ug.edu.pl wrote: >> >>> W dniu 10.12.2010 10:06, Max Horn pisze: >>>> In addition, GAP can load dynamic modules (again, at least on UNIX type >>> systems). I used that to implement some of the most time critical >>> functions of a package I am working on in C, for a major speed boost. >>> So >>> you could call other systems from within GAP >>> >>> Hello, >>> >>> How to do this? >>> Could I write my own function in C/C++, compile it into library, and use >>> in GAP? >>> I imagine that there could be necessary some types conversions (?) >>> >>> I see LoadDynamicModule() in >>> http://www.gap-system.org/Manuals/doc/htm/ref/CHAP003.htm#SECT007 >>> but is it possible to use it with library other than obtained by using >>> gac? >>> >>> >>> All the best >>> Bartosz Putrycz >> >> >> >> ------------------------------ >> >> Message: 6 >> Date: Sat, 8 Jan 2011 16:31:23 +1100 >> From: Hebert P?rez-Ros?s <hebert.pe...@gmail.com> >> To: fo...@gap-system.org >> Subject: [GAP Forum] The Add function >> Message-ID: >> <aanlktimsvw54q2vblewjv-bmecvom+d=3w3h5ex3m...@mail.gmail.com> >> Content-Type: text/plain; charset=ISO-8859-1 >> >> Dear all, >> >> I'm embarrased to say this, but I'm very puzzled by the behaviour of the >> Add >> function. I have this simple test code: >> >> -------------------------------------- >> TestFun:= function(n) >> local perm, out, i; >> >> out:= []; >> perm:= []; >> for i in [1..n] do >> perm[i]:=0; >> od; >> for i in [1..n] do >> perm[i]:= i; >> Add(out, perm); >> od; >> return out; >> end; >> ---------------------------------- >> >> If I now make a call to Test(3), I should get [ [1,0,0], [1,2,0], [1,2,3] >> ], >> right? However, I'm getting [ [1,2,3], [1,2,3], [1,2,3] ]. Do you get the >> same thing? Can anybody explain to me what's happening here? >> >> Thank you very much in advance, >> >> Hebert Perez-Roses >> The University of Newcastle, Australia >> >> >> ------------------------------ >> >> Message: 7 >> Date: Sat, 8 Jan 2011 14:01:44 +0800 >> From: Keshav Rao Kini <krk...@ntu.edu.sg> >> To: Hebert P?rez-Ros?s <hebert.pe...@gmail.com> >> Cc: "fo...@gap-system.org" <fo...@gap-system.org> >> Subject: Re: [GAP Forum] The Add function >> Message-ID: >> <aanlktinqc2aoepyeeeyx8nxezmgdm1yxtbqrk0+r=...@mail.gmail.com> >> Content-Type: text/plain; charset="utf-8" >> >> Hello, >> >> Each time you use Add, it adds perm as a new list entry in out. It does >> NOT >> add the current value of perm as a new list entry in out, but rather >> inserts >> a reference to the list perm. The list perm is added to the list out >> three >> times, and by the time the function returns, perm = [1,2,3], so out >> consists >> of three [1,2,3]. >> >> If you want to remember previous states of a list, you'll always need to >> make a copy, because this is not done automatically when using functions >> like Add. Try using for example the ShallowCopy function. >> >> Hope that helps. >> >> Yours, >> Keshav >> >> Disclaimer: the boilerplate text at the foot of this email has been added >> automatically by my mail server. This was not done by my request (rather >> the >> opposite) so please disregard it. >> >> >> >> 2011/1/8 Hebert P?rez-Ros?s >> <hebert.pe...@gmail.com<mailto:hebert.pe...@gmail.com>> >> Dear all, >> >> I'm embarrased to say this, but I'm very puzzled by the behaviour of the >> Add >> function. I have this simple test code: >> >> -------------------------------------- >> TestFun:= function(n) >> local perm, out, i; >> >> out:= []; >> perm:= []; >> for i in [1..n] do >> perm[i]:=0; >> od; >> for i in [1..n] do >> perm[i]:= i; >> Add(out, perm); >> od; >> return out; >> end; >> ---------------------------------- >> >> If I now make a call to Test(3), I should get [ [1,0,0], [1,2,0], [1,2,3] >> ], >> right? However, I'm getting [ [1,2,3], [1,2,3], [1,2,3] ]. Do you get the >> same thing? Can anybody explain to me what's happening here? >> >> Thank you very much in advance, >> >> Hebert Perez-Roses >> The University of Newcastle, Australia >> _______________________________________________ >> Forum mailing list >> Forum@mail.gap-system.org<mailto:Forum@mail.gap-system.org> >> http://mail.gap-system.org/mailman/listinfo/forum >> >> >> ________________________________ >> CONFIDENTIALITY: This email is intended solely for the person(s) named >> and >> may be confidential and/or privileged. If you are not the intended >> recipient, please delete it, notify us and do not copy, use, or disclose >> its >> content. Thank you. >> >> Towards A Sustainable Earth: Print Only When Necessary >> >> >> ------------------------------ >> >> Message: 8 >> Date: Sat, 8 Jan 2011 17:19:17 +1100 >> From: Hebert P?rez-Ros?s <hebert.pe...@gmail.com> >> To: Keshav Rao Kini <krk...@ntu.edu.sg> >> Cc: "fo...@gap-system.org" <fo...@gap-system.org> >> Subject: Re: [GAP Forum] The Add function >> Message-ID: >> <aanlkti=45xtjpxasw-97payrhfkovtvcdqd_8og4s...@mail.gmail.com> >> Content-Type: text/plain; charset=ISO-8859-1 >> >> OK, thank you very much. I would just swear that I had already tried >> that. >> Cheers, >> Hebert. >> >> >> 2011/1/8 Keshav Rao Kini <krk...@ntu.edu.sg> >> >>> Hello, >>> >>> Each time you use Add, it adds perm as a new list entry in out. It does >>> NOT >>> add the current value of perm as a new list entry in out, but rather >>> inserts >>> a reference to the list perm. The list perm is added to the list out >>> three >>> times, and by the time the function returns, perm = [1,2,3], so out >>> consists >>> of three [1,2,3]. >>> >>> If you want to remember previous states of a list, you'll always need to >>> make a copy, because this is not done automatically when using functions >>> like Add. Try using for example the ShallowCopy function. >>> >>> Hope that helps. >>> >>> Yours, >>> Keshav >>> >>> Disclaimer: the boilerplate text at the foot of this email has been >>> added >>> automatically by my mail server. This was not done by my request (rather >>> the >>> opposite) so please disregard it. >>> >>> >>> >>> 2011/1/8 Hebert P?rez-Ros?s <hebert.pe...@gmail.com> >>> >>>> Dear all, >>>> >>>> I'm embarrased to say this, but I'm very puzzled by the behaviour of >>>> the >>>> Add >>>> function. I have this simple test code: >>>> >>>> -------------------------------------- >>>> TestFun:= function(n) >>>> local perm, out, i; >>>> >>>> out:= []; >>>> perm:= []; >>>> for i in [1..n] do >>>> perm[i]:=0; >>>> od; >>>> for i in [1..n] do >>>> perm[i]:= i; >>>> Add(out, perm); >>>> od; >>>> return out; >>>> end; >>>> ---------------------------------- >>>> >>>> If I now make a call to Test(3), I should get [ [1,0,0], [1,2,0], >>>> [1,2,3] >>>> ], >>>> right? However, I'm getting [ [1,2,3], [1,2,3], [1,2,3] ]. Do you get >>>> the >>>> same thing? Can anybody explain to me what's happening here? >>>> >>>> Thank you very much in advance, >>>> >>>> Hebert Perez-Roses >>>> The University of Newcastle, Australia >>>> _______________________________________________ >>>> Forum mailing list >>>> Forum@mail.gap-system.org >>>> http://mail.gap-system.org/mailman/listinfo/forum >>>> >>> >>> >>> ------------------------------ >>> CONFIDENTIALITY: This email is intended solely for the person(s) named >>> and >>> may be confidential and/or privileged. If you are not the intended >>> recipient, please delete it, notify us and do not copy, use, or disclose >>> its >>> content. Thank you. >>> >>> Towards A Sustainable Earth: Print Only When Necessary >>> >> >> >> ------------------------------ >> >> Message: 9 >> Date: Sun, 9 Jan 2011 00:32:23 -0800 >> From: Sara Radfar <sararadfa...@gmail.com> >> To: fo...@gap-system.org >> Subject: [GAP Forum] Question >> Message-ID: >> <aanlktin5mrpg3+n3f85+dbco_nb=l_9jhj7yfjlwv...@mail.gmail.com> >> Content-Type: text/plain; charset=ISO-8859-1 >> >> Dear forum >> Hi >> I have a question about group theory.I know that should send this >> message for group pub forum but I coudn't join to it.If you can help >> me about my question: >> My question is:Let the set of the number of sylow subgroup $G$ equal >> to group $PSL(2,7)$(that is {8,21,28}) about solvability or >> unsolvability group $G$ what we can say? >> Thanks >> sara >> >> >> >> ------------------------------ >> >> _______________________________________________ >> Forum mailing list >> Forum@mail.gap-system.org >> http://mail.gap-system.org/mailman/listinfo/forum >> >> >> End of Forum Digest, Vol 86, Issue 2 >> ************************************ >> > > > -- > zahra sheikhaleslami > -- zahra sheikhaleslami _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
