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PERMUTABLE DIAGONAL-TYPE SUBGROUPS OF $G\times H$

Published online by Cambridge University Press:  01 May 2003

Joseph Evan
Joseph Evan
Affiliation:
Department of Mathematics, King's College, Wilkes-Barre, PA 18711, USA e-mail: jmevan@kings.edu
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Abstract

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Two subgroups $M$ and $S$ of a group $G$ are said to permute, or $M$permutes with$S$, if $MS = SM$. Furthermore, $M$ is a permutable subgroup of $G$ if $M$ permutes with every subgroup of $G$. In this article, we provide necessary and sufficient conditions for a subgroup of $G\times H$, whose intersections with the direct factors are normal, to be a permutable subgroup.

Keywords

20D40
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 45 , Issue 1 , January 2003 , pp. 73 - 77
Copyright
2003 Glasgow Mathematical Journal Trust