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- Title
On the semigroup rank of a group.
- Authors
Branco, Mário J. J.; Gomes, Gracinda M. S.; Silva, Pedro V.
- Abstract
For an arbitrary group G, it is known that either the semigroup rank G rk s equals the group rank G rk g , or G rk s = G rk g + 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 G rk s = G rk g + 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 (π 1 (M)) rk s = (π 1 (M)) rk g + 1 if and only if M is orientable.
- Subjects
ABELIAN groups; RANKING; FREE groups
- Publication
Semigroup Forum, 2019, Vol 99, Issue 3, p568
- ISSN
0037-1912
- Publication type
Article
- DOI
10.1007/s00233-018-9982-x