Research Article
Year 2025,
Early Access, 1 - 6
Abstract
Project Number
24ZR1422800，12471018，12171302
References
- [1] E. Detomi and A. Lucchini, Recognizing soluble groups from their probabilistic zeta functions, Bull. London Math. Soc. 35 (5), 659–664, 2003.
Year 2025,
Early Access, 1 - 6
Abstract
Let \( G \) be a finite group and \( p \) a prime. We define \( \Cc_p(G) \) as the poset of cosets of \( p \)-subgroups of \( G \), construct a probability function \( \PP_p(G,s) \) with group-theoretic connections, strengthen \cite[Theorem~D]{GuMengGuo2025-arXiv}, and analyze the connectivity of \( \Cc_p(G) \).
Supporting Institution
the Natural Science Foundation of Shanghai，the National Natural Science Foundation of China
Project Number
24ZR1422800，12471018，12171302
Thanks
The second author is supported by the Natural Science Foundation of Shanghai (24ZR1422800) and the National Natural Science Foundation of China (12471018); The third author is supported by the National Natural Science Foundation of China (12171302).
References
- [1] E. Detomi and A. Lucchini, Recognizing soluble groups from their probabilistic zeta functions, Bull. London Math. Soc. 35 (5), 659–664, 2003.
There are 1 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Group Theory and Generalisations, Topology |
| Journal Section | Mathematics |
| Authors | |
| Project Number | 24ZR1422800，12471018，12171302 |
| Early Pub Date | June 24, 2025 |
| Publication Date | |
| Submission Date | April 12, 2025 |
| Acceptance Date | May 27, 2025 |
| Published in Issue | Year 2025 Early Access |