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'...
Gespeichert in:
| Datum: | 2023 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2023
|
| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1886 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| Zusammenfassung: | 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. |
|---|