On CLT and non-CLT groups
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910361282674688 |
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| author | Tărnăuceanu, Marius |
| author_facet | Tărnăuceanu, Marius |
| contents | In this note, we prove that for every integer $d\geq 2$ which is not a prime power, there exists a finite solvable group $G$ such that $d\mid |G|$, $π(G)=π(d)$ and $G$ has no subgroup of order $d$. We also introduce the CLT-degree of a finite group and answer two questions about it. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_05774 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On CLT and non-CLT groups Tărnăuceanu, Marius Group Theory In this note, we prove that for every integer $d\geq 2$ which is not a prime power, there exists a finite solvable group $G$ such that $d\mid |G|$, $π(G)=π(d)$ and $G$ has no subgroup of order $d$. We also introduce the CLT-degree of a finite group and answer two questions about it. |
| title | On CLT and non-CLT groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2403.05774 |