
TL;DR
This paper explores the properties of Camina triples, a generalization of Camina pairs, revealing structural conditions such as nilpotency and p-group characteristics in related groups.
Contribution
It introduces the concept of Camina triples and establishes key structural results, extending the theory of Camina pairs in group theory.
Findings
If (G,N,M) is a Camina triple, then G/N is a p-group.
In a Camina triple, M is nilpotent.
M has a non-trivial nilpotent quotient.
Abstract
In this paper, we study Camina triples. Camina triples are a generalization of Camina pairs. Camina pairs were first introduced in 1978 by A.R. Camina in \cite{camina1}. Camina's work in \cite{camina1} was inspired by the study of Frobenius groups. We show that if is a Camina triple, then either is a -group, is nilpotent, or has a non-trivial nilpotent quotient.
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Taxonomy
TopicsFinite Group Theory Research · graph theory and CDMA systems · Rings, Modules, and Algebras
