On the group pseudo-algebra of finite groups
Let $G$ be a finite group. The group pseudo-algebra of $G$ is defined as the multi-set $C(G)=\lbrace (d,m_G(d))\mid d\in \mathrm{Cod} (G)\rbrace $, where $m_G(d)$ is the number of irreducible characters of $G$ with codegree $d\in \mathrm{Cod}(G)$. We show that there exist two finite $p$-groups with...
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Académie des sciences
2024-11-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.671/ |
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| author | Lewis, Mark L. Yan, Quanfu |
| author_facet | Lewis, Mark L. Yan, Quanfu |
| author_sort | Lewis, Mark L. |
| collection | DOAJ |
| description | Let $G$ be a finite group. The group pseudo-algebra of $G$ is defined as the multi-set $C(G)=\lbrace (d,m_G(d))\mid d\in \mathrm{Cod} (G)\rbrace $, where $m_G(d)$ is the number of irreducible characters of $G$ with codegree $d\in \mathrm{Cod}(G)$. We show that there exist two finite $p$-groups with distinct orders that have the same group pseudo-algebra, providing an answer to Question 3.2 in [7]. In addition, we also discuss under what hypothesis two $p$-groups with the same group pseudo-algebra will be isomorphic. |
| format | Article |
| id | doaj-art-4b73e8e591414a8d89c8fc1926f22fe7 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-4b73e8e591414a8d89c8fc1926f22fe72025-02-07T11:26:37ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-11-01362G121661166510.5802/crmath.67110.5802/crmath.671On the group pseudo-algebra of finite groupsLewis, Mark L.0Yan, Quanfu1Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USADepartment of Mathematical Sciences, Kent State University, Kent, OH 44242, USA; School of Mathematical Sciences, Peking University, Beijing, 100871, People’s Republic of ChinaLet $G$ be a finite group. The group pseudo-algebra of $G$ is defined as the multi-set $C(G)=\lbrace (d,m_G(d))\mid d\in \mathrm{Cod} (G)\rbrace $, where $m_G(d)$ is the number of irreducible characters of $G$ with codegree $d\in \mathrm{Cod}(G)$. We show that there exist two finite $p$-groups with distinct orders that have the same group pseudo-algebra, providing an answer to Question 3.2 in [7]. In addition, we also discuss under what hypothesis two $p$-groups with the same group pseudo-algebra will be isomorphic.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.671/Finite $p$-groupsCharactersGroup pseudo-algebra |
| spellingShingle | Lewis, Mark L. Yan, Quanfu On the group pseudo-algebra of finite groups Comptes Rendus. Mathématique Finite $p$-groups Characters Group pseudo-algebra |
| title | On the group pseudo-algebra of finite groups |
| title_full | On the group pseudo-algebra of finite groups |
| title_fullStr | On the group pseudo-algebra of finite groups |
| title_full_unstemmed | On the group pseudo-algebra of finite groups |
| title_short | On the group pseudo-algebra of finite groups |
| title_sort | on the group pseudo algebra of finite groups |
| topic | Finite $p$-groups Characters Group pseudo-algebra |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.671/ |
| work_keys_str_mv | AT lewismarkl onthegrouppseudoalgebraoffinitegroups AT yanquanfu onthegrouppseudoalgebraoffinitegroups |