On the conjecture of groups with the same number of centralizer
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909119900811264 |
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| author | Ahmadkhah, N. Zarrin, M. |
| author_facet | Ahmadkhah, N. Zarrin, M. |
| contents | For any group G, let $cent(G)$ denote the set of all centralizers of $G$. The authors in \cite{KZ}, Groups with the same number of centralizers,
J. Algebra Appl. (2021) 2150012 (6 pages), posed the following conjecture: Let $G$ and $S$ be finite groups.
Is it true that if $|Cent(G)|=|Cent(S)|$ and $|G'|=|S'|$, then $G$ is isoclonic to $S$? In this paper, among other things, we give a negative answer to this conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_15918 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the conjecture of groups with the same number of centralizer Ahmadkhah, N. Zarrin, M. Group Theory 20D60 For any group G, let $cent(G)$ denote the set of all centralizers of $G$. The authors in \cite{KZ}, Groups with the same number of centralizers, J. Algebra Appl. (2021) 2150012 (6 pages), posed the following conjecture: Let $G$ and $S$ be finite groups. Is it true that if $|Cent(G)|=|Cent(S)|$ and $|G'|=|S'|$, then $G$ is isoclonic to $S$? In this paper, among other things, we give a negative answer to this conjecture. |
| title | On the conjecture of groups with the same number of centralizer |
| topic | Group Theory 20D60 |
| url | https://arxiv.org/abs/2402.15918 |