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A finiteness condition for semigroups generalizing a theorem of Hotzel. (English) Zbl 0741.20038

The class of semigroups with minimum condition on principal right ideals and with locally finite maximal subgroups is locally finite. This is stronger than E. Hotzel’s finiteness theorem [J. Algebra 60, 352- 370 (1979; Zbl 0421.20032)]. The condition on subgroups can be slightly modified.
Reviewer: G.Pollák (Szeged)

MSC:

20M05 Free semigroups, generators and relations, word problems
20M12 Ideal theory for semigroups
20M07 Varieties and pseudovarieties of semigroups

Citations:

Zbl 0421.20032
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References:

[1] Blyth, R. D., Rewriting products of group elements, I, J. Algebra, 116, 506-521 (1988), see also · Zbl 0647.20033
[2] Clifford, A. H.; Preston, G. B., The Algebraic Theory of Semigroups, (Mathematical Surveys, No. 7, Vol. 2 (1967), Amer. Math. Soc: Amer. Math. Soc Providence, RI) · Zbl 0111.03403
[3] Coudrain, M.; Schützenberger, M. P., Une condition de finitude des monoides finiment engendrés, C.R. Acad. Sci. Paris Sér. A, 262, 1149-1151 (1966) · Zbl 0141.01801
[4] de Luca, A.; Restivo, A., A finiteness condition for finitely generated semigroups, (Semigroup Forum, 28 (1984)), 123-134 · Zbl 0529.20044
[5] de Luca, A.; Varricchio, S., Some combinatorial properties of the Thue-Morse sequence and a problem in semigroups, Theoret. Comput. Sci., 63, 333-348 (1989) · Zbl 0671.10050
[6] de Luca, A.; Varricchio, S., Factorial languages whose growth function is quadratically upper bounded, Inform. Process. Lett., 30, 283-288 (1989) · Zbl 0672.68034
[7] de Luca, A.; Varricchio, S., A finiteness condition for semigroups, (Proceedings of 16ème École de Printemps d’Informatique Théorique: Propriétés Formelles des Automates Finis et Applications. Proceedings of 16ème École de Printemps d’Informatique Théorique: Propriétés Formelles des Automates Finis et Applications, Lecture Notes in Computer Science, Vol. 386 (1988), Springer Verlag), 138-147
[8] Green, J. A.; Rees, D., On semigroups in which \(x^r = x\), (Math. Proc. Cambridge Philos. Soc., 48 (1952)), 35-40 · Zbl 0046.01903
[9] Gromov, M., Groups of polynomial growth and expanding maps, Inst. Hautes Études Sci. Publ. Math., 53, 53-73 (1981) · Zbl 0474.20018
[10] Hashiguchi, K., Notes on finitely generated semigroups and pumping conditions for regular languages, Theoret. Comput. Sci., 46, 53-66 (1986) · Zbl 0606.20048
[11] Hotzel, E., On finiteness conditions in semigroups, J. Algebra, 60, 352-370 (1979) · Zbl 0421.20032
[12] Lallement, G., Semigroups and Combinatorial Applications (1979), Wiley: Wiley New York · Zbl 0421.20025
[13] Petrich, M., Introduction to Semigroups (1973), Merrill: Merrill Columbus, OH · Zbl 0321.20037
[14] Restivo, A., Permutation properties and the Fibonacci semigroup, (Semigroup Forum, 38 (1989)), 337-345 · Zbl 0663.20063
[15] Restivo, A.; Reutenauer, C., On the Burnside problem for semigroups, J. Algebra, 89, 102-104 (1984) · Zbl 0545.20051
[16] Simon, I., Conditions de finitude pour des semi-groupes, C.R. Acad. Sci. Paris Sér. A, 290, 1081-1082 (1980) · Zbl 0437.20044
[17] Varricchio, S., A finiteness condition for finitely generated semigroups, (Semigroup Forum, 38 (1989)), 331-335 · Zbl 0663.20066
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