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 _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
