On the maximum order of nilpotent transitive permutation groups

TL;DR

This paper establishes an upper bound on the maximum order of finite nilpotent transitive permutation groups based on their degree and nilpotency class, advancing understanding of their structural limitations.

Contribution

It provides a new upper bound for the order of nilpotent transitive groups depending on degree and nilpotency class, which was previously unknown.

Findings

Derived an explicit upper bound as a function of n and c

Enhanced understanding of the structural constraints of nilpotent transitive groups

Potential applications in classification and symmetry analysis

Abstract

Given two positive integers n and c, we determine an upper bound, as a function of n and c, for the maximum order of a finite nilpotent transitive group of degree n and nilpotency class at most c.