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

Document Type : Research Paper

Author

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

Abstract

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.

Keywords