TY - JOUR
T1 - Profinite groups with restricted centralizers
AU - Shalev, Aner
PY - 1994/12
Y1 - 1994/12
N2 - Let G be a profinite group in which every centralizer CG(x) (x ϵ G) is either finite or of finite index. It is shown that G is finite-by-abelian-byfinite. Moreover, if, in addition, G is a just-infinite pro-p group, then it has the structure of a p-adic space group whose point group is cyclic or generalized quaternion.
AB - Let G be a profinite group in which every centralizer CG(x) (x ϵ G) is either finite or of finite index. It is shown that G is finite-by-abelian-byfinite. Moreover, if, in addition, G is a just-infinite pro-p group, then it has the structure of a p-adic space group whose point group is cyclic or generalized quaternion.
UR - http://www.scopus.com/inward/record.url?scp=53149150848&partnerID=8YFLogxK
U2 - 10.1090/S0002-9939-1994-1239805-3
DO - 10.1090/S0002-9939-1994-1239805-3
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AN - SCOPUS:53149150848
SN - 0002-9939
VL - 122
SP - 1279
EP - 1284
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 4
ER -