On groups that can be covered by conjugates of finitely many cyclic or procyclic subgroups

Yiftach Barnea; Rachel Camina; M. Ershov; Mark L. Lewis

doi:10.1007/s00208-025-03119-4

On groups that can be covered by conjugates of finitely many cyclic or procyclic subgroups

Yiftach Barnea, Rachel Camina, M. Ershov, Mark L. Lewis

Research output: Contribution to journal › Article › peer-review

Abstract

Given a discrete (resp. profinite) group G, we define to be the smallest number of cyclic (resp. procyclic) subgroups of G whose conjugates cover G. In this paper we determine all residually finite discrete groups with finite NCC and give an almost complete characterization of profinite groups with finite NCC.

Original language	English
Pages (from-to)	1747-1779
Number of pages	33
Journal	Mathematische Annalen
Volume	392
DOIs	https://doi.org/10.1007/s00208-025-03119-4
Publication status	Published - 29 Mar 2025

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Cite this

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title = "On groups that can be covered by conjugates of finitely many cyclic or procyclic subgroups",

abstract = "Given a discrete (resp. profinite) group G, we define to be the smallest number of cyclic (resp. procyclic) subgroups of G whose conjugates cover G. In this paper we determine all residually finite discrete groups with finite NCC and give an almost complete characterization of profinite groups with finite NCC.",

author = "Yiftach Barnea and Rachel Camina and M. Ershov and Lewis, \{Mark L.\}",

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T1 - On groups that can be covered by conjugates of finitely many cyclic or procyclic subgroups

AU - Barnea, Yiftach

AU - Camina, Rachel

AU - Ershov, M.

AU - Lewis, Mark L.

PY - 2025/3/29

Y1 - 2025/3/29

N2 - Given a discrete (resp. profinite) group G, we define to be the smallest number of cyclic (resp. procyclic) subgroups of G whose conjugates cover G. In this paper we determine all residually finite discrete groups with finite NCC and give an almost complete characterization of profinite groups with finite NCC.

AB - Given a discrete (resp. profinite) group G, we define to be the smallest number of cyclic (resp. procyclic) subgroups of G whose conjugates cover G. In this paper we determine all residually finite discrete groups with finite NCC and give an almost complete characterization of profinite groups with finite NCC.

U2 - 10.1007/s00208-025-03119-4

DO - 10.1007/s00208-025-03119-4

M3 - Article

SN - 0025-5831

VL - 392

SP - 1747

EP - 1779

JO - Mathematische Annalen

JF - Mathematische Annalen

ER -