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On infinite groups whose noncyclic norm has a finite index

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Abstract

We study groups in which the intersection of normalizers of all noncyclic subgroups (noncyclic norm) has a finite index. We prove that if the noncyclic norm of an infinite noncyclic group is locally graded and has a finite index in the group, then this group is central-by-finite and its noncyclic norm is a Dedekind group.

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Authors
  1. F. N. Liman
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Additional information

Sumy Pedagogical Institute, Sumy. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 5, pp. 678–684, May, 1997.

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Liman, F.N. On infinite groups whose noncyclic norm has a finite index. Ukr Math J 49, 755–762 (1997). https://doi.org/10.1007/BF02486456

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  • DOI: https://doi.org/10.1007/BF02486456

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