A note on coset complexes of $p$-subgroups

Year 2026, Issue: Advanced Online Publication, 1 - 9

Huilong Gu , Hangyang Meng , Xiuyun Guo

https://doi.org/10.15672/hujms.1674729

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 \( \Cc_p(G) \).

Keywords

Coset complexes , Probability function , M\"obius function , Connectivity.

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.