A note on the bound for the class of certain nilpotent groups
Jixia Gao, Haipeng Qu

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.
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Taxonomy
TopicsFinite Group Theory Research · graph theory and CDMA systems · Nuclear Receptors and Signaling
