Closing the relation gap by direct product stabilization

J. Harlander

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

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 languageEnglish
Pages (from-to)511-521
Number of pages11
JournalJournal of Algebra
Volume182
Issue number2
DOIs
StatePublished - 1 Jun 1996

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