This article is cited in 7 papers

Simple polyadic groups

H. Khodabandeh, M. Shahryari

University of Tabriz, Tabriz, Iran

Abstract: The main aim of this article is to establish a characterization of simple polyadic groups in terms of ordinary groups and their automorphisms. We give two different definitions of simpleness for polyadic groups, from the point of views of universal algebra, UAS (universal algebraic simpleness), and group theory, GTS (group theoretical simpleness). We obtain necessary and sufficient conditions for a polyadic group to be UAS or GTS.

Keywords: polyadic group, $n$-ary group, retract of $n$-ary group, simple polyadic group, congruence.

UDC: 512.54

Received: 04.09.2013

 English version: Siberian Mathematical Journal, 2014, 55:4, 734–744

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