Strongly reversible groups
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- by Takayuki Tamura
- Proc. Amer. Math. Soc. 84 (1982), 325-330
- DOI: https://doi.org/10.1090/S0002-9939-1982-0640223-9
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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.References
- J. L. Alperin, A classification of $n$-abelian groups, Canadian J. Math. 21 (1969), 1238–1244. MR 248204, DOI 10.4153/CJM-1969-136-1
- 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
- Alessandra Spoletini Cherubini and Ada Varisco, Sui semigruppi fortemente reversibili archimedei, Istit. Lombardo Accad. Sci. Lett. Rend. A 110 (1976), no. 2, 313–321 (1977) (Italian, with English summary). MR 492018
- Alessandra Spoletini Cherubini and Ada Varisco, Sui semigruppi fortemente reversibili separativi, Istit. Lombardo Accad. Sci. Lett. Rend. A 111 (1977), no. 1, 31–43 (1978) (Italian, with English summary). MR 507175
- A. Spoletini Cherubini and A. Varisco, On strongly reversible semigroups, Semigroup Forum 15 (1977/78), no. 3, 281–282. MR 470118, DOI 10.1007/BF02195760
- A. Cherubini Spoletini and A. Varisco, Some properties of $E-m$ semigroups, Semigroup Forum 17 (1979), no. 2, 153–161. MR 527216, DOI 10.1007/BF02194317
- Thomas Nordahl, Semigroups satisfying $(xy)^{m}=x^{m}y^{m}$, Semigroup Forum 8 (1974), no. 4, 332–346. MR 374291, DOI 10.1007/BF02194776
- Takayuki Tamura, Free $E-m$ groups and free $E-m$ semigroups, Proc. Amer. Math. Soc. 84 (1982), no. 3, 318–324. MR 640222, DOI 10.1090/S0002-9939-1982-0640222-7
- Gabriel Thierrin, Sur quelques propriétés de certaines classes de demi-groupes, C. R. Acad. Sci. Paris 239 (1954), 1335–1337 (French). MR 65551
Bibliographic Information
- © Copyright 1982 American Mathematical Society
- 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