Finite gropus whose proper subgroups of order divisible by $p$ are supersolvable

Antonio Beltrán; Fernando Viudez

Finite gropus whose proper subgroups of order divisible by $p$ are supersolvable

Group Theory 2026-07-10 v1

Authors: Antonio Beltrán , Fernando Viudez

Abstract

Let $p$ be an odd prime, and let $G$ be a finite group whose order is divisible by $p$ . Suppose that every proper subgroup of $G$ whose order is divisible by $p$ is supersolvable, while $G$ itself is not. In this paper, we investigate the arithmetic and structural properties of such groups, addressing both the solvable and nonsolvable cases.

Keywords

finite groups supersolvable groups subgroups prime divisors group structure

Cite

@article{arxiv.2607.09144,
  title  = {Finite gropus whose proper subgroups of order divisible by $p$ are supersolvable},
  author = {Antonio Beltrán and Fernando Viudez},
  journal= {arXiv preprint arXiv:2607.09144},
  year   = {2026}
}

Comments

13 pages