Solvable quotients of subdirect products of perfect groups are nilpotent

TL;DR

This paper proves that solvable quotients of subdirect products of perfect groups are necessarily nilpotent and provides examples demonstrating quotients of any nilpotency class, addressing a question posed by D. F. Holt.

Contribution

It establishes a fundamental property of solvable quotients of subdirect products of perfect groups and constructs examples with arbitrary nilpotency class.

Findings

Solvable quotients are nilpotent

Examples of quotients with any nilpotency class

Answers a question by D. F. Holt

Abstract

We prove the statement in the title and exhibit examples of quotients of arbitrary nilpotency class. This answers a question by D. F. Holt.