Combinatorial invariants for certain classes of non-abelian groups
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908744517943296 |
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| author | Godara, Naveen K. Joshi, Renu Mazumdar, Eshita |
| author_facet | Godara, Naveen K. Joshi, Renu Mazumdar, Eshita |
| contents | This article focuses on the study of zero-sum invariants of finite non-abelian groups. We address two main problems: the first centers on the ordered Davenport constant and the second on Gao's constant. We establish a connection between the ordered Davenport constant and the small Davenport constant for a finite non-abelian group of even order, which in turn gives a relation with the Noether number. Additionally, we confirm a conjecture of Gao and Li for a non-abelian group of order $2p^α$, where $p$ is a prime. Furthermore, we prove a conjecture that connects the ordered Davenport constant to the Loewy length for certain classes of finite $2$-groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13558 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Combinatorial invariants for certain classes of non-abelian groups Godara, Naveen K. Joshi, Renu Mazumdar, Eshita Combinatorics 11B75, 11P70 This article focuses on the study of zero-sum invariants of finite non-abelian groups. We address two main problems: the first centers on the ordered Davenport constant and the second on Gao's constant. We establish a connection between the ordered Davenport constant and the small Davenport constant for a finite non-abelian group of even order, which in turn gives a relation with the Noether number. Additionally, we confirm a conjecture of Gao and Li for a non-abelian group of order $2p^α$, where $p$ is a prime. Furthermore, we prove a conjecture that connects the ordered Davenport constant to the Loewy length for certain classes of finite $2$-groups. |
| title | Combinatorial invariants for certain classes of non-abelian groups |
| topic | Combinatorics 11B75, 11P70 |
| url | https://arxiv.org/abs/2408.13558 |