On identities of an \(n\)-ary group.
type: Item
instance of: scholarly article
zbMATH Open document ID: 1344.20085
DOI: 10.1142/S1793557116500297
published in: Asian-European Journal of Mathematics
publication date: 2016-05-13T00:00:00Z
Mathematics Subject Classification ID: 20N15
zbMATH DE Number: 6580470
zbMATH Keywords: \(n\)-ary groups
zbMATH Keywords: identities
zbMATH Keywords: neutral element
zbMATH Keywords: derived operations
author: A. M. Gal'mak
MaRDI profile type: Publication
cites work: Transposed vector-matrices
cites work: An abstract characteristic of matrix operatives
cites work: Q4068787
cites work: Q3708216
full work available at URL: s1793557116500297
OpenAlex ID: W2178267582
title: On identities of an \(n\)-ary group.
review text: It is very chaotic overview of results for \(n\)-ary groups with a neutral element. It is well known that an \(n\)-ary group \((G,f)\) with a neutral element (identity) has the form \(f(x_1,x_2,\ldots,x_n)=x_1x_2\cdots x_n\), where \((G,\cdot)\) is an ordinary group. Thus, the properties of \((G,f)\) are a trivial consequence of the properties of \((G,\cdot)\).NEWLINENEWLINE This overview contains a lot of typographical errors and wrong terminology. The bibliography is limited mainly to the author's earlier works published in the local Belarusian journals not indexed by Zentralblatt.
reviewed by: Wiesław A. Dudek
description: scientific article; zbMATH DE number 6580470