Group Orders That Imply a Nontrivial p-Core

2003/12/17 by Rafael Villarroel-Flores, Villarroel-Flores, Rafael
Mathematics · #20D20 #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.math/0312342

openalex publication_date 2003/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a prime number \(p\) and a natural number \(m\) not divided by \(p\), we propose the problem of finding the smallest number \(r₀\) such that for \(r≥ r₀\), every group \(G\) of order \(p^rm\) has a non-trivial normal \(p\)-subgroup. We prove that we can explicitly calculate the number \(r₀\) in the case where every group of order \(p^rm\) is solvable for all \(r\), and we obtain the value of \(r₀\) for a case where \(m\) is a product of two primes.

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