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arXiv · 1510.08251

A finiteness condition on centralizers in locally nilpotent groups

Gustavo A. Fernandez-Alcober·Leire Legarreta·Antonio Tortora·Maria Tota
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Abstract

We give a detailed description of infinite locally nilpotent groups G such that the index |C_G (x) : | is finite, for every non-normal cyclic subgroup 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.

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Gustavo A. Fernandez-Alcober, Leire Legarreta, Antonio Tortora, Maria Tota. 2015-10-28. A finiteness condition on centralizers in locally nilpotent groups. https://doi.org/10.1007/s00605-015-0854-0

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