[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5666/KMJ.2022.62.4.769

Group Orders That Imply a Nontrivial p-Core

Rafael, Villarroel-Flores (Universidad Autonoma del Estado de Hidalgo)

Publication Information

Kyungpook Mathematical Journal / v.62, no.4, 2022 , pp. 769-772 More about this Journal

Abstract

Given a prime number p and a natural number m not divisible 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.

Keywords

p-core; normal subgroups;

Citations & Related Records

Reference

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