PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 40(54), pp. 4955 (1986) 

ON $\sigma$PERMUTABLE $n$GROUPSZoran Stojakovi\'c and Wieslav A. DudekInstitut za matematiku, Novi Sad, Yugoslavia and Institute of Mathematics, Pedagogical University, 42200 Czestochowa, PolandAbstract: In this paper $\sigma$permutable $n$groups are defined and considered. An $n$group $(G,f)$ is called $\sigma$permutable, where $\sigma$ is a permutation of the set $\{1,\ldots,n+1\}$, iff $$ f(x_{\sigma 1}, \ldots, x_{\sigma n}) = x_{\sigma (n + 1)} \Leftrightarrow f(x_1, \ldots, x_n) = x_{n + 1} $$ for all $x_1,\ldots,x_{n+1}\in G$. Such $n$groups are a special case of $\sigma$permutable $n$groupoids considered in [7] and also they represent a generalization of $i$permutable $n$groups from [6] and some other classes of $n$groups. Examples of $\sigma$permutable $n$groups are given and some of their properties described. Necessary and sufficient conditions for an $n$group to be $\sigma$permutable are determined. Several conditions under which such $n$groups are derived from a binary group are given. Classification (MSC2000): 20N15 Full text of the article:
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