# [GAP Forum] Abelianizations of Subgroups

Tim Steger steger at uniss.it
Fri Jul 18 13:11:22 BST 2008

Dear GAP people,

In Section~45.14 of the manual it says:

Using variations of coset enumeration it is possible to compute the
abelian invariants of a subgroup of a finitely presented group
without computing a complete presentation for the subgroup in the
first place.

This possibility is explained a little by Havas in [Hav74b].  Suppose
we are interested only in the elementary-$p$-part of the
abelianization:

H / <[H,H] H^p> = (H / [H,H]) \otimes (Z/p)

It should be possible to calculate this using even less time and space
than the abelianization.  Is such a variant available in GAP?  In one
of the packages?  In some non-GAP program?

Yours, Tim Steger