A special characteristic decomposition of a regular semigroup S by disjoint subsemigroups is given. The subsemigroups involved in the decomposition and the interrelations among them are studied.
The concepts of T-relation, of absolute and relative -complement ( being a T-relation) are introduced for a finite group G. A necessary and sufficient condition for the conjugacy of the relative -complements of a subgroup of G is given. This result generalizes a theorem of Gaschütz.
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