Construction of a two unique product semigroup defined by permutation relations of quaternion type

Abstract

For a regular representation $H\subseteq {\text{Sym}}_n$ of the generalized quaternion group of order $n=4k$, with $k\ge 2$, the monoid $S_n(H)$ presented with generators $a_1,a_2,\dots ,a_n$ and with relations $a_1{a}_2\cdots a_n=a_{\sigma (1)}{a}_{\sigma (2)}\cdots a_{\sigma (n)}$, for all $\sigma \in H$, is investigated. It is shown that $S_n(H)$ has the two unique product property. As a consequence, for any field $K$, the monoid algebra $K[S_n(H)]$ is a domain with trivial units which is semiprimitive.

11 pages

References in corpus (1)

• Finitely Presented Monoids and Algebras defined by Permutation Relations of Abelian Type

Cited by in corpus (1)

• Finitely presented algebras defined by permutation relations of dihedral type