Finite commutative subdirectly irreducible semigroups
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- by Phillip E. McNeil PDF
- Trans. Amer. Math. Soc. 172 (1972), 57-67 Request permission
Abstract:
This paper is devoted to completing the solution to the problem of constructing all finite commutative subdirectly irreducible semigroups. Those semigroups of this type which were formerly unknown are realized as certain permutation group extensions of nilpotent semigroups. The results in this paper extend the efforts in this area by G. Thierrin and B. M. Schein.References
- Garrett Birkhoff, Subdirect unions in universal algebra, Bull. Amer. Math. Soc. 50 (1944), 764–768. MR 10542, DOI 10.1090/S0002-9904-1944-08235-9 —, Lattice theory, 2nd rev. ed., Amer. Math Soc. Colloq. Publ., vol. 25, Amer. Math. Soc., Providence, R. I., 1948. MR 10, 673.
- A. H. Clifford, Extensions of semigroups, Trans. Amer. Math. Soc. 68 (1950), 165–173. MR 33836, DOI 10.1090/S0002-9947-1950-0033836-2
- A. H. Clifford and G. B. Preston, The algebraic theory of semigroups. Vol. I, Mathematical Surveys, No. 7, American Mathematical Society, Providence, R.I., 1961. MR 0132791 P. E. McNeil, The structure of certain semigroups with two idempotents, Ph. D. Dissertation, Pennsylvania State University, University Park, Pa., 1968.
- Phillip E. McNeil, Group extensions of null semigroups, Duke Math. J. 38 (1971), 491–497. MR 285648
- B. M. Schein, Homomorphisms and subdirect decompositions of semi-groups, Pacific J. Math. 17 (1966), 529–547. MR 197603 J. T. Sedlock, Certain decompositions of periodic semigroups and congruences on nilpotent semigroups, Ph. D. Dissertation, Lehigh University, Bethlehem, Pa., 1966.
- Takayuki Tamura, The theory of construction of finite semigroups. III. Finite unipotent semigroups, Osaka Math. J. 10 (1958), 191–204. MR 102560
- Gabriel Thierrin, Sur la structure des demi-groupes, Publ. Sci. Univ. Alger. Sér. A 3 (1956), 161–171 (French). MR 100642
- Helmut Wielandt, Finite permutation groups, Academic Press, New York-London, 1964. Translated from the German by R. Bercov. MR 0183775 R. Yoshida, Ideal extensions of semigroups and compound semigroups, Mem. Res. Inst. Sci. Eng. Ritumeikan Univ. Kyoto 13 (1965), 1-8. D. Zitarelli, Subdirectly irreducible finite inverse semigroups, Ph. D. Dissertation, Pennsylvania State University, University Park, Pa., 1970.
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 172 (1972), 57-67
- MSC: Primary 20M10
- DOI: https://doi.org/10.1090/S0002-9947-1972-0310102-3
- MathSciNet review: 0310102