Abstract
In this article, we introduce the notion of representations of polyadic groups and we investigate the connection between these representations and those of retract groups and covering groups.
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Borowiec, A., Dudek, W.A., Duplij, S.: Bi-element representations of ternary groups. Commun. Algebra 34, 1651–1670 (2006)
Dörnte, W.: Unterschungen über einen verallgemeinerten Gruppenbegriff. Math. Z. 29, 1–19 (1929)
Dudek, W.A.: Remarks on n-groups. Demonstr. Math. 13, 165–181 (1980)
Dudek, W.A.: On n-ary group with only one skew element. Rad. Mat. (Sarajevo) 6, 171–175 (1990)
Dudek, W.A., Glazek, K.: Around the Hosszú–Gluskin Theorem for n-ary groups. Discrete Math. 308, 4861–4876 (2008)
Dudek, W.A., Glazek, K., Gleichgewicht, B.: A note on the axioms of n-groups. Colloq. Math. Soc. János Bolyai 29, 195–202 (1977)
Dudek, W.A., Michalski, J.: On a generalization of Hosszú theorem. Demonstr. Math. 15, 437–441 (1982)
Dudek, W.A., Michalski, J.: On retract of polyadic groups. Demonstr. Math. 17, 281–301 (1984)
Głazek, K., Gleichgewicht, B.: Abelian n-groups. Colloq. Math. Soc. János Bolyai 29, 321–329 (1977)
Gleichgewicht, B., Wanke-Jakubowska, M.B., Wanke-Jerie, M.E.: On representations of cyclic n-groups. Demonstr. Math. 16, 357–365 (1983)
Grzymala-Busse, J.W.: Automorphisms of polyadic automata. J. Assoc. Comput. Mach. 16, 208–219 (1969)
Kasner, E.: An extension of the group concept. Bull. Am. Math. Soc. 10, 290–291 (1904)
Kerner, R.: Ternary and non-associative algebraic structures and their applications in physics. Univ. P. and M. Curie, Paris (2000)
Michalski, J.: Covering k-groups of n-groups. Arch. Math. (Brno) 17, 207–226 (1981)
Nikshych, D., Vainerman, L.: Finite quantum groupoids and their applications. Univ. California, Los Angeles (2000)
Pojidaev, A.P.: Enveloping algebras of Fillipov algebras. Commun. Algebra 31, 883–900 (2003)
Post, E.L.: Polyadic groups. Trans. Am. Math. Soc. 48, 208–350 (1940)
Vainerman, L., Kerner, R.: On special classes of n-algebras. J. Math. Phys. 37, 2553–2565 (1996)
Wanke-Jakubowska, M.B., Wanke-Jerie, M.E.: On representations of n-groups. Ann. Sci. Math. Polonae. Comment. Math. 24, 335–341 (1984)
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Dudek, W.A., Shahryari, M. Representation Theory of Polyadic Groups. Algebr Represent Theor 15, 29–51 (2012). https://doi.org/10.1007/s10468-010-9231-9
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DOI: https://doi.org/10.1007/s10468-010-9231-9