6 papers
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…
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,…
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…
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…
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…
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…