Note on semigroups, which are semilattices of groups
Soukup Lajos · Proceedings of the Japan Academy Series A Mathematical Sciences · 1968
Let S be a semigroup.Following the terminology o A. H. Clifford [1], [2] we say that S is a semilattice of groups if S is a set- theoretical union of a set {G, a e I) of mutually disjoint subgroups G such that, for every or, /9 in I, the products GG and GG are both contained in the same Gr (y e I).Recently the author proved the following characterization o semi- groups, which are semilattices of groups (see [3]).Theorem 1.A semigroup S is a semilattice of groups if and only if ( 1 )