
Journal of Lie Theory 15 (2005), No. 1, 235248 Copyright Heldermann Verlag 2005 Topologically Locally Finite Groups with a CCSubgroup Zvi Arad Department of Mathematics, BarIlan University, RamatGan, Israel aradtzvi@macs.biu.ac.il Wolfgang Herfort Institute of Analysis and Scientific Computation, University of Technology, Vienna, Austria wolfgang.herfort@tuwien.ac.at [Abstractpdf] A proper subgroup $M$ of a finite group $G$ is called a CCsubgroup 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 CCsubgroup'' [Communications in Algebra 32 (2004) 20872098] the present authors, having taken all this work into account, classified all finite groups containing a CCsubgroup. \endgraf As an application, in the present paper, we classify totally disconnected topologically locally finite groups, containing a topological analogue of a CCsubgroup. Keywords: CCsubgroups, prime graph, compactness conditions, locally compact groups. MSC: 22D05; 20E18, 20F50 [ Fulltextpdf (209 KB)] for subscribers only. 