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 -