关于可被有限个循环或pro循环子群的共轭覆盖的群
群论
2025-02-07 v3 数论
摘要
给定一个离散（或pro有限）群 ，我们定义 为覆盖 所需的 的循环（或pro循环）子群的共轭的最小数目。本文我们确定了所有具有有限 NCC 的剩余有限离散群，并给出了具有有限 NCC 的 pro有限群的几乎完整的刻画。
引用
@article{arxiv.2210.15746,
title = {On groups that can be covered by conjugates of finitely many cyclic or procyclic subgroups},
author = {Yiftach Barnea and Rachel Camina and Mikhail Ershov and Mark L. Lewis},
journal= {arXiv preprint arXiv:2210.15746},
year = {2025}
}
备注
v3: 30 pages, to appear in Math. Annalen. Major revision based on the referee's report. Sections 6 and 7 have been completely rewritten. We have also removed the results from the original paper dealing with NCC for families of finite p-groups or relied on computations in the group PGL_1(D) where D is the quaternion division algebra over Q_p. We plan to include those results in a follow-up paper