A new characterization of $A_{p}$ with $p $ and $p-2$ are twin primes
Let $G$ be a finite group and $\pi_{e}(G)$ be the set of elements order of $G$. Let $k \in \pi_{e}(G)$ and $m_{k}$ be the number of elements of order $k$ in $G$. Set nse($G$):=$\{ m_{k} | k \in \pi_{e}(G)\}$. Assume $p$ and $p-2$ are twin primes. We prove that if $G$ is a group such that nse($G$)=ns...
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| Format: | Article |
| Language: | English |
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Sociedade Brasileira de Matemática
2015-09-01
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| Series: | Boletim da Sociedade Paranaense de Matemática |
| Subjects: | |
| Online Access: | http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/24335 |
| _version_ | 1818481023323734016 |
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| author | Seyed Sadegh Salehi Amiri Alireza Khalili Asboei |
| author_facet | Seyed Sadegh Salehi Amiri Alireza Khalili Asboei |
| author_sort | Seyed Sadegh Salehi Amiri |
| collection | DOAJ |
| description | Let $G$ be a finite group and $\pi_{e}(G)$ be the set of elements order of $G$. Let $k \in \pi_{e}(G)$ and $m_{k}$ be the number of elements of order $k$ in $G$. Set nse($G$):=$\{ m_{k} | k \in \pi_{e}(G)\}$. Assume $p$ and $p-2$ are twin primes. We prove that if $G$ is a group such that nse($G$)=nse($A_{p}$) and $p\in \pi (G)$, then $G \cong A_{p}$. As a consequence of our results we prove that $A_{p}$ is uniquely determined by its nse and order. |
| first_indexed | 2024-12-10T11:29:57Z |
| format | Article |
| id | doaj.art-814249af7b5547eb8dbe7b82b5d67be0 |
| institution | Directory Open Access Journal |
| issn | 0037-8712 2175-1188 |
| language | English |
| last_indexed | 2024-12-10T11:29:57Z |
| publishDate | 2015-09-01 |
| publisher | Sociedade Brasileira de Matemática |
| record_format | Article |
| series | Boletim da Sociedade Paranaense de Matemática |
| spelling | doaj.art-814249af7b5547eb8dbe7b82b5d67be02022-12-22T01:50:38ZengSociedade Brasileira de MatemáticaBoletim da Sociedade Paranaense de Matemática0037-87122175-11882015-09-0133223124010.5269/bspm.v33i2.2433511544A new characterization of $A_{p}$ with $p $ and $p-2$ are twin primesSeyed Sadegh Salehi Amiri0Alireza Khalili Asboei1Azad University, Babol Department of MathematicsFarhangian University Department of MathematicsLet $G$ be a finite group and $\pi_{e}(G)$ be the set of elements order of $G$. Let $k \in \pi_{e}(G)$ and $m_{k}$ be the number of elements of order $k$ in $G$. Set nse($G$):=$\{ m_{k} | k \in \pi_{e}(G)\}$. Assume $p$ and $p-2$ are twin primes. We prove that if $G$ is a group such that nse($G$)=nse($A_{p}$) and $p\in \pi (G)$, then $G \cong A_{p}$. As a consequence of our results we prove that $A_{p}$ is uniquely determined by its nse and order.http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/24335Element orderset of the numbers of elements of the same orderalternating group |
| spellingShingle | Seyed Sadegh Salehi Amiri Alireza Khalili Asboei A new characterization of $A_{p}$ with $p $ and $p-2$ are twin primes Boletim da Sociedade Paranaense de Matemática Element order set of the numbers of elements of the same order alternating group |
| title | A new characterization of $A_{p}$ with $p $ and $p-2$ are twin primes |
| title_full | A new characterization of $A_{p}$ with $p $ and $p-2$ are twin primes |
| title_fullStr | A new characterization of $A_{p}$ with $p $ and $p-2$ are twin primes |
| title_full_unstemmed | A new characterization of $A_{p}$ with $p $ and $p-2$ are twin primes |
| title_short | A new characterization of $A_{p}$ with $p $ and $p-2$ are twin primes |
| title_sort | new characterization of a p with p and p 2 are twin primes |
| topic | Element order set of the numbers of elements of the same order alternating group |
| url | http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/24335 |
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