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
aradtzvi@macs.biu.ac.il
Wolfgang Herfort
Institute of Analysis and Scientific Computation, University of Technology, Vienna, Austria
wolfgang.herfort@tuwien.ac.at
[Abstract-pdf]
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
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