Acta Mathematica Vietnamica
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Anticentral and Antisemicentral Elements of Infinite Soluble Groups
Bertram Arthur Frederick Wehrfritzpp. 147-154
Abstract
An element $a$ of a group $G$ is said to be anticentral in $G$ if $G^\prime = \{[g, a] \,:\, g ∈ G\}$ and antisemicentral in $G$ if $\{[g,a] \,:\, g ∈ G\}$ contains a normal subgroup of $G$ of finite index in $G^\prime$. We study such elements in various types of infinite soluble group.