On infinite groups whose noncyclic norm has a finite index
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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.
KeywordsQuotient Group Abelian Subgroup Cyclic Subgroup Finite Index Periodic Part
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