Abstract
A theorem of Polovickiĭ states that any group with finitely many normalizers of subgroups is finite over its centre. Here we prove that the centre of a non-periodic group G has finite index if and only if G has finitely many normalizers of non-periodic subgroups.
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This work was done while the authors were supported by MIUR — PRIN2007 (Teoria dei Gruppi e Applicazioni).
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De Falco, M., de Giovanni, F. & Musella, C. Groups with finitely many normalizers of non-periodic subgroups. Rend. Circ. Mat. Palermo 59, 289–294 (2010). https://doi.org/10.1007/s12215-010-0022-2
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DOI: https://doi.org/10.1007/s12215-010-0022-2