On the maximal subgroups of almost simple and primitive perfect groups

Patricia Medina Capilla; Luca Sabatini

doi:10.1017/s0305004126102175

July 29, 2026Mathematical Proceedings of the Cambridge Philosophical SocietyOpen Access

On the maximal subgroups of almost simple and primitive perfect groups

View Full Paper

Ask AI

Bookmark

Share

Key Points

The study aims to demonstrate that the 10th term of the derived series of maximal subgroups of finite almost simple groups is perfect.
Proved properties using derived series in group theory
Analyzed specific characteristics of maximal subgroups
Investigated the structure of finite almost simple groups
The 10th term of the derived series of maximal subgroups of almost simple groups is proven to be perfect.
This property also holds if the group G is perfect and H is core-free.
The constant 10 is established as the best possible in this context.

Ask about this paper

Answers are grounded in this paper and cite their sources.

Implication

This research proves that the 10th term of the derived series of maximal subgroups is perfect in almost simple groups, indicating a strong structural property.

Abstract

We prove that, if G is a finite almost simple group and H is a maximal subgroup of G , then the 10th term of the derived series of H is perfect. The same is true if G is perfect and H is core-free. The constant 10 is best possible.

Discussion

No takes yet. Share an insight, caveat, or question.

Cite This Study

Capilla et al. (2026) studied this question.

synapsesocial.com/papers/6a6c472e747664a1aa73c256 https://doi.org/10.1017/s0305004126102175

View Full Paper

Ask AI

Bookmark

Share

On the maximal subgroups of almost simple and primitive perfect groups

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

On the maximal subgroups of almost simple and primitive perfect groups

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

Keep reading

Keep reading