The inverse monoid associated to a group and the semidirect product of groups

Document Type: Research Paper


Laboratory of Pure and Applied Mathematics , Department of Mathematics, University of M'sila, B.P 166, Msila, Algeria


In this paper, we construct an inverse monoid $M\left( G\right) $ associated
to a given group $G$ by using the notion of the join of subgroups and then,
by applying the left action of monoid $M$ on a semigroup $S$, we form a
semigroup $S\omega M$ on the set $S\times M$. The finally result is to build
the semi direct product of groups associated to the group action on an
another group.