On n-Levi groups
type: Item
instance of: scholarly article
title: On n-Levi groups
zbMATH Open document ID: 0605.20033
DOI: 10.1007/BF01191994
author: Luise-Charlotte Kappe
published in: Archiv der Mathematik
publication date: 1986-01-01T00:00:00Z
review text: Let G be a group. G is called an n-abelian group if \((xy)^ n=x^ ny^ n\) for the integer n and all x,y\(\in G\). G is called an n-Levi group if \((x^ n,y)=(x,y)^ n\) for the integer n and all x,y\(\in G\). G is called an n-Bell group if \((x^ n,y)=(x,y^ n)\) for the integer n and all x,y\(\in G.\) The exponent semigroup of G is defined as the set of all integers n so that G is n-abelian. The Levi semigroup of G is defined as the set of all integers n so that G is n-Levi. The Bell semigroup of G is defined as the set of all integers n so that G is n-Bell. The author obtains arithmetic characterizations of the exponent semigroup of G, the Levi semigroup of G, and the Bell semigroup of G. She finds in Theorem 1, her main result, that these characterizations are the same in all three cases. She concludes by deriving consequences of Theorem 1 and exhibiting interesting examples.
Mathematics Subject Classification ID: 20F12
Mathematics Subject Classification ID: 20F45
Mathematics Subject Classification ID: 20M10
zbMATH DE Number: 3977257
zbMATH Keywords: n-abelian group
zbMATH Keywords: n-Levi group
zbMATH Keywords: n-Bell group
zbMATH Keywords: exponent semigroup
zbMATH Keywords: Levi semigroup
zbMATH Keywords: Bell semigroup
zbMATH Keywords: arithmetic characterizations
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3977257