The automorphism group of a class of semi-groups

Abstract

Let (S,-) be a semi-group having the following properties: (1) S= U S~ where ~ is in some index set I and S~ are subgroups isomorphic to each other, (2) S~ (~ S~ = 0, a void set for ~ =fi fl and (3) the identity of S~ is a left identity of S for each ~ in I. Then the automorphism group Aut (S) of S is studied from the point of category theory. It is proved that Aut (S) is determined by Aut(S~) and right multiplications by the identities of groups S~.