[GAP Forum] commutator relations in p-group
Stefan Kohl
kohl at mathematik.uni-stuttgart.de
Wed Nov 24 16:59:40 GMT 2004
Dear Forum,
Siddhartha Sarkar wrote:
> I need to know the classification of p-groups satisfy the following
> commutator relation:
>
> (1) say the group G is minimally generated by d elements
> x_1, x_2,...,x_d.
> (2) if d is even, the relation is [x_1, x_2]...[x_{d-1},x_d] = 1
> (3) for d odd, the relation is [x_1, x_2]...[x_d,x] = 1
> for some element x in G.
Your condition is relatively weak --
A pc-presentation of a p-group of order p^n requires n(n+1)/2 relations.
Out of these you prescribe only one.
Given that there are asymptotically p^((2/27)n^3) isomorphism types
of groups of order p^n, it seems likely that there also is a huge
number of p-groups which satisfy your relation, and that it does not
make sense to attempt to classify them in general.
Bettina Eick has already suggested you off-list to use NQ or ANUPQ --
maybe these packages help you in investigating your problem.
By the way: when replying to Forum digests, please make sure that
you only cite the relevant part. Thanks!
Best wishes,
Stefan Kohl
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