JP Journal of Algebra, Number Theory and Applications
Volume 7, Issue 1, Pages 83 - 95
(February 2007)
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GROUPS WITH FINITELY MANY NORMALIZERS OF INFINITE INDEX
Fausto De Mari (Italy) and Francesco De Giovanni (Italy)
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Abstract: A famous theorem of B. H. Neumann states that a group G is central-by-finite if and only if all normalizers of subgroups of G have finite index, and Y. D. Polovickii proved that this is also equivalent to the property that the group G has only finitely many normalizers of subgroups. Here the structure of groups in which all but finitely many normalizers of (in-finite) subgroups have finite index is investigated, and the above results are extended to this more general situation. |
Keywords and phrases: normalizer subgroup, almost normal subgroup |
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