On the semigroup rank of a group

• Tipo: Artigo em Revista Científica Internacional
• Data: 2019

Autores

Branco, MJJ (Autor) Outra; Gomes, GMS (Autor) Outra; Pedro V. Silva (Autor) FCUP

Revista

Título: Semigroup Forum

Vol. 99

Páginas: 568-578

ISSN: 0037-1912

Editora: Springer Nature

Indexação

ISI Web of Knowledge - 0 Citações

Scopus - 0 Citações

Outras Informações

ID Authenticus: 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.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 11