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