THE INVERSE MONOID ASSOCIATED TO A GROUP AND THE SEMIDIRECT PRODUCT OF GROUPS

In this paper, we construct an inverse monoid M (G) 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 SωM on the set S × M. The finally result is to build the semi direct product of groups associated to the group action on an another group.