Topologically Locally Finite Groups with a CC-Subgroup

Zvi Arad and Wolfgang Herfort

Abstract: A proper subgroup $M$ of a finite group $G$ is called a CC-subgroup of $G$ if the centralizer $C_G(m)$ of every $m\in M^{#}=M\setminus\{1\}$ is contained in $M$. Such finite groups had been partially classified by S. Williams, A. S. Kondrat'iev, N. Iiyori and H. Yamaki, M. Suzuki, W. Feit and J. G.Thompson, M. Herzog, Z. Arad, D. Chillag and others. In "Classification of Finite Groups with a CC-subgroup, Communications in Algebra 32 (2004), 2087–2098" the present authors, having taken all this work into account, classified all finite groups containing a CC-subgroup. \endgraf As an application, in the present paper, we classify totally disconnected topologically locally finite groups, containing a topological analogue of a CC-subgroup.

Classification (MSC2000): 22D05, 20E18, 20F50

Full text of the article: (for faster download, first choose a mirror)

• PDF file (212 kilobytes)