TY - JOUR

T1 - Topologically locally finite groups with a CC-subgroup

AU - Arad, Zvi

AU - Herfort, Wolfgang

PY - 2005

Y1 - 2005

N2 - A proper subgroup M of a finite group G is called a CC-subgroup of G if the centralizer CG(m) of every m ε M#=M \{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 [6] the present authors, having taken all this work into account, classified all finite groups containing a CC-subgroup. As an application, in the present paper, we classify totally disconnected topologically locally finite groups, containing a topological analogue of a CC-subgroup.

AB - A proper subgroup M of a finite group G is called a CC-subgroup of G if the centralizer CG(m) of every m ε M#=M \{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 [6] the present authors, having taken all this work into account, classified all finite groups containing a CC-subgroup. As an application, in the present paper, we classify totally disconnected topologically locally finite groups, containing a topological analogue of a CC-subgroup.

KW - CC-subgroups

KW - Compactness conditions

KW - Locally compact groups

KW - Prime graph

UR - http://www.scopus.com/inward/record.url?scp=12744266527&partnerID=8YFLogxK

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AN - SCOPUS:12744266527

SN - 0949-5932

VL - 15

SP - 235

EP - 248

JO - Journal of Lie Theory

JF - Journal of Lie Theory

IS - 1

ER -