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PERMUTABLE DIAGONAL-TYPE SUBGROUPS OF $G\times H$
Published online by Cambridge University Press: 01 May 2003
Abstract
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.
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- 2003 Glasgow Mathematical Journal Trust
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