Camina p-groups that are generalized Frobenius complements

2014/11/12 by I. M. Isaacs, Mark L. Lewis, Isaacs, I. M. +1
Mathematics · #20D10 #20D15 #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras #Secondary 20C15 #math.GR #msc:20C15 #msc:20D10 #msc:20D15

paper · pdf · doi:10.48550/arxiv.1411.3278

This fixes a mistake in the paper `Classifying Camina groups: a theorem of Dark and Scoppola'

arxiv created 2014/11/12 · openalex publication_date 2014/11/12 · arxiv updated 2014/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let P be a Camina p-group that acts on a group Q in such a way that C_P (x) ⊆ P' for all nonidentity elements x ∈ Q. We show that P must be isomorphic to the quaternion group Q₈. If P has class 2, this is a known result, and this paper corrects a previously published erroneous proof of the general case.

Related

• Camina triples
• A Frobenius group analog for Camina triples
• Camina pairs that are not p-closed
• On automorphisms of finite p-groups
• MVW-extensions of real quaternionic classical groups