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.
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
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!
Darci L. Kracht
Department of Mathematics and Computer Science
Kent State University
Kent, OH USA