A finiteness condition on centralizers in locally nilpotent groups

Abstract

We give a detailed description of infinite locally nilpotent groups G such that the index |C_G (x) : <x>| is finite, for every non-normal cyclic subgroup <x> of G. We are also able to extend our analysis to all non-periodic groups satisfying a variation of our condition, where the requirement of finiteness is replaced with a bound.

10 pages, submitted to an international journal. arXiv admin note: substantial text overlap with arXiv:1412.7330

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• A finiteness condition on centralizers in locally nilpotent groups

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• A finiteness condition on centralizers in locally nilpotent groups