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- Title
Generators and presentations for direct and wreath products of monoid acts.
- Authors
Miller, Craig
- Abstract
We investigate the preservation of the properties of being finitely generated and finitely presented under both direct and wreath products of monoid acts. A monoid M is said to preserve property P in direct products if, for any two M-acts A and B, the direct product A × B has property P if and only if both A and B have property P . It is proved that the monoids M that preserve finite generation (resp. finitely presentability) in direct products are precisely those for which the diagonal M-act M × M is finitely generated (resp. finitely presented). We show that a wreath product A ≀ B is finitely generated if and only if both A and B are finitely generated. It is also proved that a necessary condition for A ≀ B to be finitely presented is that both A and B are finitely presented. Finally, we find some sufficient conditions for a wreath product to be finitely presented.
- Subjects
WREATH products (Group theory); MONOIDS; MANUFACTURED products
- Publication
Semigroup Forum, 2020, Vol 100, Issue 1, p315
- ISSN
0037-1912
- Publication type
Article
- DOI
10.1007/s00233-018-9987-5