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

In this paper, we construct an inverse monoid M\left( G\right) associatedto 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 asemigroup S\omega M on the set S\times M. The finally result is to buildthe semi direct product of groups associated to the group action on ananother group.

کلیدواژه ها:

Semigroup ، idempotents of semigroup ، inverses of semigroup