非阿贝尔循环群中最小乘积集
星系天体物理
2025-05-15 v1 高能天体物理现象
摘要
给定有限群G和正整数r和s，代数中的一个感兴趣问题是确定乘积集AB的最小基数，其中A和B是G的子集且|A|=r且|B|=s。该问题已为阿贝尔群解决；然而，对有限非阿贝尔群仍未解决。本文证明，阿贝尔群的结果可推广到循环群K_{m,n}=\langle a,b \ : \ a^m=1,b^{2n}=a^g,bab^{-1}=a^{-1}\rangle。因此，我们为二面体群D_n和四元环群Q_{4n}提供了新的证明。
引用
@article{arxiv.2505.08885,
title = {XMM-Newton Conclusively Identifies an Active Galactic Nucleus in a Green Pea Galaxy},
author = {Peter G. Boorman and Jiří Svoboda and Daniel Stern and Bret D. Lehmer and Abhijeet Borkar and Murray Brightman and Hannah P. Earnshaw and Fiona A. Harrison and Konstantinos Kouroumpatzakis and Barbora Adamcová and Roberto J. Assef and Matthias Ehle and Brian Grefenstette and Romana Grossová and Maitrayee Gupta and Elias Kammoun and Taiki Kawamuro and Lea Marcotulli and Romana Mikušincová and Matthew J. Middleton and Edward Nathan and Joanna M. Piotrowska and Jean J. Somalwar and Núria Torres-Albà and Dominic J. Walton and Daniel R. Weisz},
journal= {arXiv preprint arXiv:2505.08885},
year = {2025}
}
备注
Accepted for publication in ApJ. 21 pages (27 including appendix and bibliography), 11 figures