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# Combinatorially Factorizable Cryptic Inverse Semigroups

Published:2014-06-16
Printed: Sep 2014
• Mario Petrich,
21420 Bol, Brač, Croatia
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## Abstract

An inverse semigroup $S$ is combinatorially factorizable if $S=TG$ where $T$ is a combinatorial (i.e., $\mathcal{H}$ is the equality relation) inverse subsemigroup of $S$ and $G$ is a subgroup of $S$. This concept was introduced and studied by Mills, especially in the case when $S$ is cryptic (i.e., $\mathcal{H}$ is a congruence on $S$). Her approach is mainly analytical considering subsemigroups of a cryptic inverse semigroup. We start with a combinatorial inverse monoid and a factorizable Clifford monoid and from an action of the former on the latter construct the semigroups in the title. As a special case, we consider semigroups which are direct products of a combinatorial inverse monoid and a group.
 Keywords: inverse semigroup, cryptic semigroup
 MSC Classifications: 20M18 - Inverse semigroups