Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2508.11776 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912539624865792 |
|---|---|
| author | Das, Arpan Kanrar, Arpan |
| author_facet | Das, Arpan Kanrar, Arpan |
| contents | Inspired by a conjecture by Guarnieri and Vendramin concerning the number of braces with a generalized quaternion adjoint group, many researchers have studied braces whose adjoint group is a non-abelian $2$-group with a cyclic subgroup of index $2$. Following this direction, braces with generalized quaternion, dihedral, and semidihedral adjoint groups have been classified. It was found that the number of such braces stabilizes as the group order increases. In this paper, we consider the remaining open case of modular maximal-cyclic groups. We show that these braces possess only one non-cyclic additive group structure, and, in contrast to previous findings, the number of such braces increases with increasing order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_11776 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Modular maximal-cyclic braces Das, Arpan Kanrar, Arpan Group Theory Quantum Algebra 16T25, 20H25, 20K30, 20D15 Inspired by a conjecture by Guarnieri and Vendramin concerning the number of braces with a generalized quaternion adjoint group, many researchers have studied braces whose adjoint group is a non-abelian $2$-group with a cyclic subgroup of index $2$. Following this direction, braces with generalized quaternion, dihedral, and semidihedral adjoint groups have been classified. It was found that the number of such braces stabilizes as the group order increases. In this paper, we consider the remaining open case of modular maximal-cyclic groups. We show that these braces possess only one non-cyclic additive group structure, and, in contrast to previous findings, the number of such braces increases with increasing order. |
| title | On Modular maximal-cyclic braces |
| topic | Group Theory Quantum Algebra 16T25, 20H25, 20K30, 20D15 |
| url | https://arxiv.org/abs/2508.11776 |