Xiaofang Gao

collaborators

3 papers

math.GR2025

On pyramidal groups whose number of involutions is a prime power

Xiaofang Gao, Martino Garonzi

A Kirkman Triple System $I^$ is called $m$ -pyramidal if there exists a subgroup $G$ of the automorphism group of $I^$ that fixes $m$ points and acts regularly on the other points.…

math.GR2024

On small Sylow numbers of finite groups

Xiaofang Gao, Igor Lima, Rulin Shen

Let $G$ be a finite group and $n_{p} (G)$ the number of Sylow $p$ -subgroups of $G$ . In this paper, we prove if $n_{p} (G) < p^{2}$ then almost all numbers $n_{p} (G)$ are a power of a prime.

math.GR2024

Bounds in terms of the number of cyclic subgroups

Xiaofang Gao, Martino Garonzi

A family of groups is called (maximal) cyclic bounded ((M)CB) if, for every natural number $n$ , there are only finitely many groups in the family with at most $n$ (maximal) cyclic…