Back to Search
Start Over
Generators and presentations for direct and wreath products of monoid acts
- Publication Year :
- 2018
-
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 $\mathcal{P}$ in direct products if, for any two $M$-acts $A$ and $B$, the direct product $A\times B$ has property $\mathcal{P}$ if and only if both $A$ and $B$ have property $\mathcal{P}$. 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 $M\times M$ is finitely generated (resp. finitely presented). We show that a wreath product $A\wr B$ is finitely generated if and only if both $A$ and $B$ are finitely generated. It is also proved that a necessary condition for $A\wr B$ 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.<br />Comment: arXiv admin note: text overlap with arXiv:1709.08916
- Subjects :
- Mathematics - Group Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1804.03010
- Document Type :
- Working Paper