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Strongly reversible groups


Author: Takayuki Tamura
Journal: Proc. Amer. Math. Soc. 84 (1982), 325-330
MSC: Primary 20E34; Secondary 20M10
DOI: https://doi.org/10.1090/S0002-9939-1982-0640223-9
MathSciNet review: 640223
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Abstract | References | Similar Articles | Additional Information

Abstract: Following Thierrin [9], a group $ G$ is called strongly reversible if for every $ x$, $ y \in G$ there are positive integers $ l$, $ m$, $ n$ such that $ {(xy)^l} = {x^m}{y^n} = {y^n}{x^m}$. This paper studies the structure of strongly reversible groups.


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  • [1] J. L. Alperin, A classification of $ n$-abelian groups, Canad. J. Math. 21 (1969), 1238-1244. MR 0248204 (40:1458)
  • [2] A. H. Clifford and G. B. Preston, Algebraic theory of semi-groups, Math. Surveys, no. 7, Amer. Math. Soc., Providence, R. I., 1961, pp. 1-224. MR 0132791 (24:A2627)
  • [3] A. S. Cherubini and A. Varisco, Sui semigruppi fortemente reversibili archimedei, Istit. Lombardo Accad. Sci. Lett. Rend A 110 (1976), 313-321. MR 0492018 (58:11182)
  • [4] -, Sui semigruppi fortemente reversibili separanvi, Istit. Lombardo Accad. Sci. Lett. Rend. A 111 (1977), 31-43. MR 0507175 (58:22360)
  • [5] -, On strongly reversible semigroups, Semigroup Forum 15 (1978), 281-282. MR 0470118 (57:9885)
  • [6] -, Some properties of $ E{\text{ - }}m$ semigroups, Semigroup Forum 17 (1979), 153-161. MR 527216 (80c:20087)
  • [7] T. Nordahl, Semigroups satisfying $ {(xy)^m} = {x^m}{y^m}$, Semigroup Forum 8 (1974), 332-346. MR 0374291 (51:10491)
  • [8] T. Tamura, Free $ E{\text{ - }}m$ groups and free $ E{\text{ - }}m$ semigroups, Proc. Amer. Math. Soc.84 (1982), 318-324. MR 640222 (83c:20070)
  • [9] G. Thierin, Sur quelques propriétés de certaines classes de demi-groupes, C. R. Acad. Sci. Paris 239 (1954), 1335-1337. MR 0065551 (16:443e)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0640223-9
Keywords: Strongly reversible groups, $ E{\text{ - }}m$ groups, $ E{\text{ - }}m$ semigroups
Article copyright: © Copyright 1982 American Mathematical Society

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