On Sigma-permutable N-groups
Publications de l'Institut Mathématique, _N_S_40 (1986) no. 54, p. 49
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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}, łdots, x_{\sigma n}) = x_{\sigma (n + 1)}
Łeftrightarrow f(x_1, łdots, 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 :
20N15
@article{PIM_1986_N_S_40_54_a5,
author = {Zoran Stojakovi\'c and Wieslav A. Dudek},
title = {On {Sigma-permutable} {N-groups}},
journal = {Publications de l'Institut Math\'ematique},
pages = {49 },
publisher = {mathdoc},
volume = {_N_S_40},
number = {54},
year = {1986},
language = {en},
url = {http://geodesic.mathdoc.fr/item/PIM_1986_N_S_40_54_a5/}
}
Zoran Stojaković; Wieslav A. Dudek. On Sigma-permutable N-groups. Publications de l'Institut Mathématique, _N_S_40 (1986) no. 54, p. 49 . http://geodesic.mathdoc.fr/item/PIM_1986_N_S_40_54_a5/