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Dear Gap-Forum,

I am just learning to use GAP and I cannot figure out how

to enter the types of groups ("algebra groups") that I'm working

on. (Finite) Algebra groups are p-groups that are constructed from

finite-dimensional nilpotent algebras over finite fields. (Every-

thing that I look at is finite!)

For example, I might have an algebra J over a finite field F (here

F=GF(q) where q is a power of a prime p) generated by two (non-

commuting) symbols x and y with various relations. (Maybe J^4=0

and y^3=0 and yx-xy-y^2=0, for example).

To get my group G, I just define G=1+J (where 1 is a multiplicative

identity elt in some larger algebra containing J). Note that J is

the Jacobson Radical of the algebra F*1+J. Then G is a finite p-group.

What I want to do right now is to determine the normalizers of certain

algebra subgroups of G (say H = 1+Fy+Fy^2, for example).

I have learned to do a few things with GAP, but not exactly what I need.

Specifically:

1) I have managed to get a finitely presented algebra with the appropriate

generators and relations, but it's always Unital.

2) Also, some of the functions (from the VE package) don't work if q is

not prime. This is the case I need since my conjecture is trivial

if q is prime.

3) Finally, I have no idea how to tell GAP to construct the group from

the algebra.

I suppose I could represent my groups as matrices, but it's much easier

for what I am doing to use generators and relations.

Any hints or suggestions would be most welcome!

Thanks.

Darci L. Kracht

Department of Mathematics and Computer Science

Kent State University

Kent, OH USA

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