A note on the bound for the class of certain nilpotent groups

TL;DR

This paper establishes the precise upper bound for the nilpotency class of a specific class of nilpotent groups where all proper subgroups have class at most 3, advancing understanding of their structural limits.

Contribution

It provides the exact upper bound for the nilpotency class of groups with the given subgroup class constraints, a previously unresolved problem.

Findings

Determined the exact upper bound of the nilpotency class for the specified groups.

Clarified the relationship between subgroup classes and the overall group class.

Enhanced theoretical understanding of nilpotent group structures.

Abstract

Assume G is a nilpotent group of class > 3 in which every proper subgroup has class at most 3. In this note, we give the exact upper bound of class of G.