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Dear forum,

it is evident that the associated Lie algebra of a modular group algebra of,

for example , a dihedral group of order 128 over GF(2) is Lie nilpotent. As

you could see below, this result is confirmed by LAG share package, but

without LAG we obtained the negative answer. Is this a bug or I am doing

something wrong in the 1st part of the test ?

1.)

gap> G:=DihedralGroup(128);

<pc group of size 128 with 7 generators>

gap> F:=GF(2);

GF(2)

gap> FG:=GroupRing(F,G);

<algebra-with-one over GF(2), with 7 generators>

gap> L:=LieAlgebra(FG);

<Lie algebra of dimension 128 over GF(2)>

gap> IsLieNilpotent(L);

false

2.)

gap> RequirePackage("lag");

true

gap> FH:=GroupRing(F,G);

<algebra-with-one over GF(2), with 7 generators>

gap> M:=LieAlgebra(FH);

<Lie algebra over GF(2)>

gap> IsLieNilpotent(M);

true

Sincerely yours,

Alexander B. Konovalov,

Zaporozhye State University, Zaporozhye, Ukraine.

E-mail: konovalov@member.ams.org

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