Journal Home Page

Cumulative Index

List of all Volumes

Complete Contents
of this Volume

Previous Article

Next Article

Journal of Lie Theory 15 (2005), No. 1, 235--248
Copyright Heldermann Verlag 2005

Topologically Locally Finite Groups with a CC-Subgroup

Zvi Arad
Department of Mathematics, Bar-Ilan University, Ramat-Gan, Israel

Wolfgang Herfort
Institute of Analysis and Scientific Computation, University of Technology, Vienna, Austria


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.

Keywords: CC-subgroups, prime graph, compactness conditions, locally compact groups.

MSC: 22D05; 20E18, 20F50

[ Fulltext-pdf  (209  KB)] for subscribers only.