TL;DR
This paper investigates properties of semi-p-abelian groups, disproving a conjecture for p=3 and confirming it for metabelian semi-p-abelian groups, thereby clarifying their structural characteristics.
Contribution
The paper disproves the conjecture that semi-p-abelian groups are strongly semi-p-abelian for p=3 and establishes the conjecture's validity for metabelian semi-p-abelian groups.
Findings
Disproved the conjecture for p=3.
Confirmed the conjecture for metabelian semi-p-abelian groups.
Clarified the structural properties of semi-p-abelian groups.
Abstract
The conjecture that semi-p-abelian groups is strongly semi-p-abelian is flase for p=3.And it's true for metabelian semi-p-abelian groups.
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Taxonomy
TopicsRings, Modules, and Algebras