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.

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