Year: 2024
Type: article
Abstract: 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 a group need not be p-solvable, and we study its structure by proving that only one nonabelian simple group of order divisible by p, which belongs to the family $$\textrm{PSL}_n(q)$$ PSL n ( q ) , can be involved in it. For $$p=2$$ p = 2 , we specify more, and in fact, such a simple group must be isomorphic to $$\textrm{PSL}_2({r^a})$$ PSL 2 ( r a ) for certain values of the prime r and the parameter a.
Authors: Antonio Beltrán, Changguo Shao
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,990
Award: G7388561198
OpenAlex ID: W4405804894