This paper reports, without proof, that if S1 and S2 are finite semigroups and if their power semigroups are isomorphic, then S1 and S2 are isomorphic; and also reports some results on the study of g-classes of the power semigroups of finite O-simple semigroups. The detailed proofs will be published elsewhere [21], [22], [23].

On the power semigroup of the group of integers

On the Recent Results in the Study of Power Semigroups

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This book, along with volume I, which appeared previously, presents a survey of the structure and representation theory of semi groups. Volume II goes more deeply than was possible in volume I into the theories of minimal ideals in a semi group, inverse semi groups, simple semi groups, congruences on a semi group, and the embedding of a semi group in a group. Among the more important recent developments of which an extended treatment is presented are B. M. Sain's theory of the representations of an arbitrary semi group by partial one-to-one transformations of a set, L. Redei's theory of finitely generated commutative semi groups, J. M. Howie's theory of amalgamated free products of semi groups, and E. J. Tully's theory of representations of a semi group by transformations of a set. Also a full account is given of Malcev's theory of the congruences on a full transformation semi group.

On the power semigroup of the group of integers

Citations

On the Recent Results in the Study of Power Semigroups

References

The algebraic theory of semigroups

Introduction to semigroups

On the maximal semilattice decomposition of the power semigroup of a semigroup

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