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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2401.07834 |
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| _version_ | 1866916213439856640 |
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| author | Blackburn, Simon R. Cocke, William Misseldine, Andrew Venkataraman, Geetha |
| author_facet | Blackburn, Simon R. Cocke, William Misseldine, Andrew Venkataraman, Geetha |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07834 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exponent-Critical Groups Blackburn, Simon R. Cocke, William Misseldine, Andrew Venkataraman, Geetha Group Theory 20D10, 20D15, 20E10 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. |
| title | Exponent-Critical Groups |
| topic | Group Theory 20D10, 20D15, 20E10 |
| url | https://arxiv.org/abs/2401.07834 |