Finite solvable tidy Groups whose orders are divisible by two primes
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917572082925568 |
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| author | Beike, Nicolas F. Carleton, Rachel Costanzo, David G. Heath, Colin Lewis, Mark L. Lu, Kaiwen Pearce, Jamie D. |
| author_facet | Beike, Nicolas F. Carleton, Rachel Costanzo, David G. Heath, Colin Lewis, Mark L. Lu, Kaiwen Pearce, Jamie D. |
| contents | In this paper, we investigate finite solvable tidy groups. We classify the tidy $\{ p, q \}$-groups. Combining this with a previous result, we are able to characterize the finite tidy solvable groups. Using this characterization, we bound the Fitting height of finite tidy solvable groups and we prove that the quotients of finite tidy solvable groups are tidy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_11476 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite solvable tidy Groups whose orders are divisible by two primes Beike, Nicolas F. Carleton, Rachel Costanzo, David G. Heath, Colin Lewis, Mark L. Lu, Kaiwen Pearce, Jamie D. Group Theory Primary: 20D10 Secondary: 20D20 In this paper, we investigate finite solvable tidy groups. We classify the tidy $\{ p, q \}$-groups. Combining this with a previous result, we are able to characterize the finite tidy solvable groups. Using this characterization, we bound the Fitting height of finite tidy solvable groups and we prove that the quotients of finite tidy solvable groups are tidy. |
| title | Finite solvable tidy Groups whose orders are divisible by two primes |
| topic | Group Theory Primary: 20D10 Secondary: 20D20 |
| url | https://arxiv.org/abs/2401.11476 |