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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2503.18285 |
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| _version_ | 1866910890108911616 |
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| author | Herman, Allen Kaur, Surinder |
| author_facet | Herman, Allen Kaur, Surinder |
| contents | Assume $F$ is a finite field of order $p^f$ and $q$ is an odd prime for which $p^f-1=sq^m$, where $m \ge 1$ and $(s,q)=1$. In this article, we obtain the order of symmetric and unitary subgroup of the semisimple group algebra $FC_q.$ Further, for the extension $G$ of $C_q = \langle b \rangle$ by an abelian group $A$ of order $p^n$ with $C_{A}(b) = \{e\}$, we prove that if $m>1,$ or $(s+1) \geq q$ and $2n \geq f(q-1)$, then $G$ does not have a normal complement in $V(FG)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18285 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the normal complement problem for finite group algebras of Abelian-by-cyclic groups Herman, Allen Kaur, Surinder Rings and Algebras 16U60 (Primary) 20C05, 20E45 (Secondary) Assume $F$ is a finite field of order $p^f$ and $q$ is an odd prime for which $p^f-1=sq^m$, where $m \ge 1$ and $(s,q)=1$. In this article, we obtain the order of symmetric and unitary subgroup of the semisimple group algebra $FC_q.$ Further, for the extension $G$ of $C_q = \langle b \rangle$ by an abelian group $A$ of order $p^n$ with $C_{A}(b) = \{e\}$, we prove that if $m>1,$ or $(s+1) \geq q$ and $2n \geq f(q-1)$, then $G$ does not have a normal complement in $V(FG)$. |
| title | On the normal complement problem for finite group algebras of Abelian-by-cyclic groups |
| topic | Rings and Algebras 16U60 (Primary) 20C05, 20E45 (Secondary) |
| url | https://arxiv.org/abs/2503.18285 |