Mathematical logic, algebra and number theory

Periodic locally nilpotent groups of finite $c$-dimension

A. A. Buturlakin^a, I. E. Devyatkova<sup>b

a</sup> Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk, 630090, Russia
^b Novosibirsk State University, 1, Pirogova str., Novosibirsk, 630090, Russia

Abstract: According to Bryant's theorem a periodic locally nilpotent group satisfying minimal condition on centralizers is virtually nilpotent. The $c$-dimension of a group is the supremum of lengths of chains of centralizers. We bound the index of the nilpotent radical of a locally nilpotent $p$-group of finite $c$-dimension $k$ in terms of $k$ and $p$.

Keywords: $c$-dimension, periodic locally nilpotent group, locally nilpotent $p$-group.

UDC: 512.54

MSC: 20E15, 20F50

Received November 29, 2019, published August 18, 2020

Language: English

DOI: 10.33048/semi.2020.17.083

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