activity
20242026
collaborators

6 papers

math.GR2026

Finite groups with simple or -nilpotent maximal subgroups

Antonio Beltrán, Fernando Viudez

Let be a prime number. When is odd, we study finite groups in which every maximal subgroup is either non-abelian simple or -nilpotent, as well as those in which every ma…

math.GR2026

Finite groups whose proper subgroups of order divisible by are supersolvable

Antonio Beltrán, Fernando Viudez

Let be an odd prime, and let be a finite group whose order is divisible by . Suppose that every proper subgroup of whose order is divisible by is supersolvable,…

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 is a prime or the square of a prime, then 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

A criterion for a normal subgroup to be hypercentral based on class sizes

Antonio Beltrán

Let be a finite group and a normal subgroup of . We prove that the knowledge of the sizes of the conjugacy classes of that are contained in and of their multipli…

math.GR2024

p-Nilpotent maximal subgroups in finite groups

Antonio Beltrán, Changguo Shao

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