On the semigroup rank of a group

• Type: Article in International Scientific Journal
• Date: 2019

Authors

Branco, MJJ (Author) Other; Gomes, GMS (Author) Other; Pedro V. Silva (Author) FCUP

Journal

Title: Semigroup Forum

Vol. 99

Pages: 568-578

ISSN: 0037-1912

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 0 Citations

Scopus - 0 Citations

Other information

Authenticus ID: P-00P-WCP

DOI: 10.1007/s00233-018-9982-x

Abstract (EN): For an arbitrary group G, it is known that either the semigroup rank Grks equals the group rank Grkg, or Grks=Grkg+1. This is the starting point for the research of the article, where the precise relation between both ranks for diverse kinds of groups is established. The semigroup rank of any relatively free group is computed. For a finitely generated abelian group G, it is proved that Grks=Grkg+1 if and only if G is torsion-free. In general, this is not true. Partial results are obtained in the nilpotent case. It is also shown that if M is a connected closed surface, then (pi 1(M))rks=(pi 1(M))rkg+1 if and only if M is orientable.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 11