Changguo Shao

collaborators

4 papers

math.GR2025

Supersolvable subgroups of order divisible by 3

Antonio BeltrÃ¡n, Changguo Shao

We determine the structure of the finite non-solvable groups of order divisible by $3$ all whose maximal subgroups of order divisible by $3$ are supersolvable. Precisely, we demons…

math.GR2025

Indices of non-supersolvable maximal subgroups in finite groups

Antonio BeltrÃ¡n, Changguo Shao

Two classic results, due to K. Doerk and P. Hall respectively, establish the solvability of those finite groups all of whose maximal subgroups are supersolvable, and the solvabilit…

math.GR2025

Extensions of a theorem of P. Hall on indexes of maximal subgroups

Antonio BeltrÃ¡n, Changguo Shao

We extend a classical theorem of P. Hall that claims that if the index of every maximal subgroup of a finite group $G$ is a prime or the square of a prime, then $G$ is solvable. Pr…

math.GR2024

p-Nilpotent maximal subgroups in finite groups

Antonio BeltrÃ¡n, Changguo Shao

Let $p$ be a prime number and suppose that every maximal subgroup of a finite group is either $p$ -nilpotent or has prime index. Such group need not be $p$ -solvable, and we study it…