Exponent-critical groups

Simon R. Blackburn; William Cocke; Andrew Misseldine; Geetha Venkataraman

doi:10.1515/jgth-2024-0177

Exponent-critical groups

Simon R. Blackburn, William Cocke, Andrew Misseldine, Geetha Venkataraman

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Journal	Journal of Group Theory
Early online date	24 Jan 2025
DOIs	https://doi.org/10.1515/jgth-2024-0177
Publication status	E-pub ahead of print - 24 Jan 2025

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10.1515/jgth-2024-0177

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Cite this

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