Orbit isomorphic skeleton groups
Recent development in the classification of \(p\)-groups often concentrate on the coclass graph \(\mathcal{G}(p,r)\) associated with the finite \(p\)-groups coclass \(r\), specially on periodicity results on these graphs. In particular, the structure of the subgraph induced by `skeleton groups'...
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| Дата: | 2023 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2023
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1886 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-18862023-10-30T03:23:03Z Orbit isomorphic skeleton groups Saha, S. finite groups, \(p\)-groups, coclass 20D15, 20D99 Recent development in the classification of \(p\)-groups often concentrate on the coclass graph \(\mathcal{G}(p,r)\) associated with the finite \(p\)-groups coclass \(r\), specially on periodicity results on these graphs. In particular, the structure of the subgraph induced by `skeleton groups' is of notable interest. Given their importance, in this paper, we investigate periodicity results of skeleton groups. Our results concentrate on the skeleton groups in \(\mathcal{G}(p,1)\). We find a family of skeleton groups in \(\mathcal{G}(7,1)\) whose \(6\)-step parent is not a periodic parent. This shows that the periodicity results available in the current literature for primes \(p\equiv 5\bmod 6\) do not hold for the primes \(p\equiv 1\bmod 6\). We also improve a known periodicity result in a special case of skeleton groups. Lugansk National Taras Shevchenko University Monash University RTP Scholarship, Australia 2023-10-12 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1886 10.12958/adm1886 Algebra and Discrete Mathematics; Vol 35, No 2 (2023) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1886/pdf Copyright (c) 2023 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
finite groups \(p\)-groups coclass 20D15 20D99 |
| spellingShingle |
finite groups \(p\)-groups coclass 20D15 20D99 Saha, S. Orbit isomorphic skeleton groups |
| topic_facet |
finite groups \(p\)-groups coclass 20D15 20D99 |
| format |
Article |
| author |
Saha, S. |
| author_facet |
Saha, S. |
| author_sort |
Saha, S. |
| title |
Orbit isomorphic skeleton groups |
| title_short |
Orbit isomorphic skeleton groups |
| title_full |
Orbit isomorphic skeleton groups |
| title_fullStr |
Orbit isomorphic skeleton groups |
| title_full_unstemmed |
Orbit isomorphic skeleton groups |
| title_sort |
orbit isomorphic skeleton groups |
| description |
Recent development in the classification of \(p\)-groups often concentrate on the coclass graph \(\mathcal{G}(p,r)\) associated with the finite \(p\)-groups coclass \(r\), specially on periodicity results on these graphs. In particular, the structure of the subgraph induced by `skeleton groups' is of notable interest. Given their importance, in this paper, we investigate periodicity results of skeleton groups. Our results concentrate on the skeleton groups in \(\mathcal{G}(p,1)\). We find a family of skeleton groups in \(\mathcal{G}(7,1)\) whose \(6\)-step parent is not a periodic parent. This shows that the periodicity results available in the current literature for primes \(p\equiv 5\bmod 6\) do not hold for the primes \(p\equiv 1\bmod 6\). We also improve a known periodicity result in a special case of skeleton groups. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2023 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1886 |
| work_keys_str_mv |
AT sahas orbitisomorphicskeletongroups |
| first_indexed |
2024-04-12T06:25:41Z |
| last_indexed |
2024-04-12T06:25:41Z |
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1796109207782555648 |