Geodesic
Topologically Locally Finite Groups with a CC-Subgroup
Journal of Lie Theory, Tome 15 (2005) no. 1, pp. 235-248

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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 : 22D05, 20E18, 20F50
Mots-clés : CC-subgroups, prime graph, compactness conditions, locally compact groups 
Z. Arad; W. Herfort. Topologically Locally Finite Groups with a CC-Subgroup. Journal of Lie Theory, Tome 15 (2005) no. 1, pp. 235-248. http://geodesic.mathdoc.fr/item/JOLT_2005_15_1_a15/
@article{JOLT_2005_15_1_a15,
     author = {Z. Arad and W. Herfort},
     title = {Topologically {Locally} {Finite} {Groups} with a {CC-Subgroup}},
     journal = {Journal of Lie Theory},
     pages = {235--248},
     year = {2005},
     volume = {15},
     number = {1},
     zbl = {1062.22008},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2005_15_1_a15/}
}
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