Groups with many self-centralizing subgroups
Primo\v z Moravec
University of Ljubljana
Costantino Delizia
University of Salerno, Italy
Heiko Dietrich
Monash University, Australia
Urban Jezernik
IMFM, Slovenia
Chiara Nicotera
University of Salerno, Italy
Chris Parker
University of Birmingham, UK
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Minisymposium: APPLICATIONS OF GROUPS IN GRAPH THEORY
Content: A subgroup $H$ of a group $G$ is called self-centralizing if $C_G(H)$ is contained in $H$. In this talk we describe finite groups in which every non-cyclic subgroup is self-centralizing, and apply this information to certain classes of infinite groups with the same property. We also consider groups in which every non-abelian subgroup is self-centralizing, and address the problem of classification of finite $p$-groups with this property that was posed by Berkovich.