On the finite images of finitely generated perfect groups

TL;DR

This paper explores the existence of a finitely generated perfect group capable of mapping onto all finite d-generated perfect groups, proving a special case involving groups with specific subnormal series.

Contribution

It introduces a conjecture about universal finitely generated perfect groups and proves a special case related to groups with bounded subnormal series and specific factors.

Findings

Proposes a conjecture on finitely generated perfect groups with universal properties.

Proves a special case for groups with bounded subnormal series and abelian or semisimple factors.

Advances understanding of the structure and images of perfect groups.

Abstract

Let $d \geq 2$ be an integer. We conjecture that there is a finitely generated perfect group whose homomorphic images include all finite $d$-generated perfect groups. We prove a special case of this conjecture for the finite perfect groups with a subnormal series of bounded length and factors which are abelian or semisimple.