On the cohomological triviality of the center of the Frattini subgroup

2022/11/02 by Jaime Calles, José Cantarero, Calles, Jaime +5 · 1 citation
Computer Science · Engineering · Mathematics · #20D15 #20J05 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2211.00865

openalex publication_date 2022/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We improve the existing lower bounds on the order of counterexamples to a conjecture by P. Schmid, determine some properties of the possible counterexamples of minimum order for each prime, and the isomorphism type of the center of the Frattini subgroup for the counterexamples of order 256. We also show that nonabelian metacyclic p-groups, nonabelian groups of maximal nilpotency class and 2-groups of coclass two satisfy the conjecture.

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