On when a topologically simple semigroup is simple

Abstract

AbstractThe compact semigroups in which each topologically simple subsemigroup is simple are characterized as those in which no subgroup sontains an element of infinite order. It is also shown that a locally compact toplogically simple subsemigroup of a compact semigroup must be simple. The note closes with an open problem.Subject classification (Amer. Math. Soc. (MOS) 1970): primary 22 A 15; secondary 20 M 10.