TY - JOUR
T1 - Centralizers in residually finite torsion groups
AU - Shalev, Aner
PY - 1998
Y1 - 1998
N2 - Let G be a residually finite torsion group. We show that, if G has a finite 2-subgroup whose centralizer is finite, then G is locally finite. We also show that, if G has no 2-torsion, and Q is a finite 2-group acting on G in such a way that the centralizer CG(Q) is soluble, or of finite exponent, then G is locally finite.
AB - Let G be a residually finite torsion group. We show that, if G has a finite 2-subgroup whose centralizer is finite, then G is locally finite. We also show that, if G has no 2-torsion, and Q is a finite 2-group acting on G in such a way that the centralizer CG(Q) is soluble, or of finite exponent, then G is locally finite.
UR - http://www.scopus.com/inward/record.url?scp=22444452203&partnerID=8YFLogxK
U2 - 10.1090/s0002-9939-98-04471-2
DO - 10.1090/s0002-9939-98-04471-2
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AN - SCOPUS:22444452203
SN - 0002-9939
VL - 126
SP - 3495
EP - 3499
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 12
ER -