Abstract
Locally nilpotent groups in which the centralizer of some finitely generated subgroup has finite rank are studied. It is shown that if G is such a group and F is a finitely generated subgroup with centralizer CG(F) of finite rank, then the centralizer of the image of F in the factor group G/t(G) modulo the periodic part t(G) also has finite rank. It is also shown that G is hypercentral when F is cyclic and either G is torsion-free or all Sylow subgroups of the periodic part of CG(F) are finite.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 11, pp. 1511–1517, November, 1992.
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Onishchuk, V.A. Locally nilpotent groups with a centralizer of finite rank. Ukr Math J 44, 1390–1394 (1992). https://doi.org/10.1007/BF01071513
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DOI: https://doi.org/10.1007/BF01071513