INDICABLE GROUPS AND ENDOMORPHIC PRESENTATIONS


Benli M. G.

GLASGOW MATHEMATICAL JOURNAL, vol.54, no.2, pp.335-344, 2012 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 54 Issue: 2
  • Publication Date: 2012
  • Doi Number: 10.1017/s0017089511000632
  • Journal Name: GLASGOW MATHEMATICAL JOURNAL
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.335-344

Abstract

In this paperwe look at presentations of subgroups of finitely presented groups with infinite cyclic quotients. We prove that if H is a finitely generated normal subgroup of a finitely presented group G with G/H cyclic, then H has ascending finite endomorphic presentation. It follows that any finitely presented indicable group without free semigroups has the structure of a semidirect product H (sic) Z, where H has finite ascending endomorphic presentation.