Dear Alexander, Dear forum Thank you very much.
On Thu, Dec 7, 2017 at 7:11 PM, Alexander Konovalov < alexander.konova...@st-andrews.ac.uk> wrote: > > > On 7 Dec 2017, at 13:19, Surinder Kaur <surinder.k...@iitrpr.ac.in> > wrote: > > > > Dear Forum, Dear Alexander Konovalov, > > > > I wanted to calculate the size of the centralizer of an element of V(FG) > in FG, when F is a finite field with 3 elements and G is a non-abelain > group of order 3^3. I am unable to do this even with the help of LAGUNA > package. It is showing that it is "beyond its memory limit." > > It's not surprising - you will either run out of memory or run out of time > if you will try a straightforward approach. > > However, you can do efficient calculations of normalisers in the unit group > given as a pc group: > > gap> g:=SmallGroup(3^3,3);; > gap> f:=GF(3);; > gap> fg:=GroupRing(f,g);; > gap> v:=PcNormalizedUnitGroup(fg); > <pc group of size 2541865828329 with 26 generators> > gap> s:=Random(v); > f2^2*f5*f6*f8*f10*f11*f13*f14*f17*f20^2*f24*f25^2 > gap> Centraliser(v,s); > <pc group of size 4782969 with 14 generators> > > and then you only have to deduce how its centraliser in FG looks like. > > Hope this helps, > Alexander > > > > On Mon, Dec 4, 2017 at 3:34 PM, Alexander Konovalov < > alexander.konova...@st-andrews.ac.uk> wrote: > > Dear Surinder, > > > > You have 3^27 elements in fg, and 3^26 of them of augmentation one, so > the calculation > > which you're trying to perform is not feasible. You need to use the > LAGUNA package > > to be able work with normalised unit group of fg in a very efficient pc > presentation > > and then interpret the result in terms of fg. See, for example, a sample > calculation > > at https://gap-packages.github.io/laguna/doc/chap2.html > > > > For example, in your setup, you can find the minimal generating set of > the > > normalised unit group as follows: > > > > gap> g:=SmallGroup(3^3,3);; > > gap> f:=GF(3);; > > gap> fg:=GroupRing(f,g);; > > gap> u:=NormalizedUnitGroup(fg); > > <group of size 2541865828329 with 26 generators> > > gap> v:=PcNormalizedUnitGroup(fg); > > <pc group of size 2541865828329 with 26 generators> > > gap> MinimalGeneratingSet(v); > > [ f1, f2, f3, f4, f6, f7, f9, f12, f21, f26 ] > > gap> gens:=MinimalGeneratingSet(v); > > [ f1, f2, f3, f4, f6, f7, f9, f12, f21, f26 ] > > gap> phi:=NaturalBijectionToNormalizedUnitGroup(fg);; > > gap> List(gens,x -> x^phi); > > [ (Z(3)^0)*f1, (Z(3)^0)*f2, (Z(3))*<identity> of > ...+(Z(3)^0)*f2+(Z(3)^0)*f2^ > > 2, (Z(3))*<identity> of ...+(Z(3))*f1+(Z(3))*f2+(Z(3)^0)*f1*f2, > > (Z(3))*<identity> of ...+(Z(3)^0)*f1+(Z(3)^0)*f1^2, > > (Z(3)^0)*f1+(Z(3))*f2+(Z(3)^0)*f1*f2+(Z(3))*f2^2+(Z(3)^0)*f1*f2^2, > > (Z(3))*f1+(Z(3)^0)*f2+(Z(3))*f1^2+(Z(3)^0)*f1*f2+(Z(3)^0)*f1^2*f2, > > (Z(3))*<identity> of ...+(Z(3)^0)*f1+(Z(3)^0)*f2+(Z(3)^0)*f1^2+(Z(3)^ > > 0)*f1*f2+(Z(3)^0)*f2^2+(Z(3)^0)*f1^2*f2+(Z(3)^0)*f1*f2^2+( > Z(3)^0)*f1^ > > 2*f2^2, (Z(3))*f1+(Z(3))*f2+(Z(3)^0)*f3+(Z(3))*f1^2+(Z(3))*f1*f2+( > Z(3)^ > > 0)*f1*f3+(Z(3))*f2^2+(Z(3)^0)*f2*f3+(Z(3))*f1^2*f2+(Z(3)^0)* > f1^2*f3+( > > Z(3))*f1*f2^2+(Z(3)^0)*f1*f2*f3+(Z(3)^0)*f2^2*f3+(Z(3))*f1^ > 2*f2^2+(Z(3)^ > > 0)*f1^2*f2*f3+(Z(3)^0)*f1*f2^2*f3+(Z(3)^0)*f1^2*f2^2*f3, > > (Z(3))*<identity> of ...+(Z(3)^0)*f1+(Z(3)^0)*f2+( > Z(3)^0)*f3+(Z(3)^0)*f1^ > > 2+(Z(3)^0)*f1*f2+(Z(3)^0)*f1*f3+(Z(3)^0)*f2^2+(Z(3)^0)*f2* > f3+(Z(3)^0)*f3^ > > 2+(Z(3)^0)*f1^2*f2+(Z(3)^0)*f1^2*f3+(Z(3)^0)*f1*f2^2+(Z(3) > ^0)*f1*f2*f3+( > > Z(3)^0)*f1*f3^2+(Z(3)^0)*f2^2*f3+(Z(3)^0)*f2*f3^2+(Z(3)^0)* > f1^2*f2^2+( > > Z(3)^0)*f1^2*f2*f3+(Z(3)^0)*f1^2*f3^2+(Z(3)^0)*f1*f2^2*f3+(Z(3)^ > > 0)*f1*f2*f3^2+(Z(3)^0)*f2^2*f3^2+(Z(3)^0)*f1^2*f2^2*f3+(Z(3)^0)*f1^ > > 2*f2*f3^2+(Z(3)^0)*f1*f2^2*f3^2+(Z(3)^0)*f1^2*f2^2*f3^2 ] > > > > Please do not hesitate ask me if you will have further questions. > > > > Best regards, > > Alexander > > > > > > > On 4 Dec 2017, at 05:47, Surinder Kaur <surinder.k...@iitrpr.ac.in> > wrote: > > > > > > Dear Forum > > > > > > I wanted to get some information in GAP about the elements of > augmentation > > > 1 in the group algebra FG, where F is a Galois field with 3 elements > and G > > > is non-abelian of order 3^3. > > > > > > I am trying this way: > > > > > > g:=SmallGroup(3^3,3);; > > > f:=GF(3);; > > > fg:=GroupRing(f,g);; > > > e:=Identity(fg);; > > > m:=MinimalGeneratingSet(g);; > > > v:=Filtered(fg,x->Augmentation(x) = Z(3)^0);; > > > Print (v[1], "\n"); > > > > > > > > > But I am getting that "it has reached pre-set memory limit". > > > > > > How can I get the elements of v. Any suggestion will be highly > appreciated. > > > > > > -- > > > > > > *Regards**Surinder Kaur* > > > *Research scholar * > > > *Department of Mathematics * > > > *IIT Ropar* > > > > > > > > > > -- > > Regards > > Surinder Kaur > > Research scholar > > Department of Mathematics > > IIT Ropar > > -- > Dr. Alexander Konovalov, Senior Research Fellow > Centre for Interdisciplinary Research in Computational Algebra (CIRCA) > School of Computer Science, University of St Andrews > Software Sustainability Institute Fellow > https://alexk.host.cs.st-andrews.ac.uk > -- > The University of St Andrews is a charity registered in > Scotland:No.SC013532 > > > -- *Regards* *Surinder Kaur* *Research scholar * *Department of Mathematics * *IIT Ropar* _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum