Changguo Shao

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20242026

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5 papers · 1 filter

math.GR2026

Finite groups with conjugacy classes of size $2 p^{n}$

Antonio Beltran, Changguo shao

We extend Burnside's $p^{a}$ -Theorem on conjugacy classes of prime-power size by proving that no non-abelian finite simple group possesses a conjugacy class of size $2 p^{n}$ for any pr…

math.GR2025

Supersolvable subgroups of order divisible by 3

Antonio Beltrán, 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

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

Antonio Beltrán, 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.GR2025

Indices of non-supersolvable maximal subgroups in finite groups

Antonio Beltrán, 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.GR2024

p-Nilpotent maximal subgroups in finite groups

Antonio Beltrán, 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…

Finite groups with conjugacy classes of size 2pn

Supersolvable subgroups of order divisible by 3

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

Indices of non-supersolvable maximal subgroups in finite groups

p-Nilpotent maximal subgroups in finite groups

Finite groups with conjugacy classes of size $2 p^{n}$