Abstract
The generation gap of a group G is the difference between the minimal number of generators of G and the rank of the augmentation ideal. The relation gap of a presentation F/N is the difference between the minimal number of elements that generate N as a normal subgroup and the minimal number of G-module generators of the relation module N/[N, N]. We show that if G is a finitely presented group then there exists n such that G × Π ni = 1 Zp, Zp being the cyclic group of order p, has zero generation and zero relation gap. We apply this result to questions concerning the efficiency of finite groups.
Original language | English |
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Pages (from-to) | 511-521 |
Number of pages | 11 |
Journal | Journal of Algebra |
Volume | 182 |
Issue number | 2 |
DOIs | |
State | Published - 1 Jun 1996 |