Exponent-Critical Groups

2024/01/15 by Simon R. Blackburn⋆, Blackburn, Simon R., William Cocke +5
Computer Science · Mathematics · #20D10 #20D15 #20E10 #Advanced Graph Theory Research #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2401.07834

openalex publication_date 2024/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define and investigate the property of being `exponent-critical' for a finite group. A finite group is said to be exponent-critical if its exponent is not the least common multiple of the exponents of its proper non-abelian subgroups. We explore properties of exponent-critical groups and give a characterization of such groups. This characterization generalises a classical result of Miller and Moreno on minimal non-abelian groups; interesting families of p-groups appear.

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