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

M3 - Article

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 -