Solvable groups satisfying the two-prime hypothesis II

TL;DR

This paper investigates solvable groups satisfying the two-prime hypothesis, establishing an upper bound on their conjugacy class count under specific conditions, and extends the result from previous work.

Contribution

It proves a new bound on the number of conjugacy classes for certain solvable groups satisfying the two-prime hypothesis, generalizing earlier findings.

Findings

Bound of 462,515 on conjugacy classes for groups with no nonabelian nilpotent quotients

Extension of previous results to broader class of solvable groups

Confirmation that the bound applies to all such groups

Abstract

In this paper, we consider solvable groups that satisfy the two-prime hypothesis. We prove that if $G$ is such a group and $G$ has no nonabelian nilpotent quotients, then $|\cd G| \le 462,515$. Combining this result with the result from part I, we deduce that if $G$ is any such group, then the same bound holds.