Unit groups of the finite group algebras of generalized quaternion groups

Sahai, Meena; Ansari, Sheere Farhat

doi:10.1142/s0219498820501121

Cited by 2 publications

(3 citation statements)

References 7 publications

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“…Certain properties of the group of normalized units of the modular group algebras of these groups were studied in [1,2]. Moreover, the structures of the semisimple group algebras of these groups have been obtained in [17,21].…”

Section: Introductionmentioning

confidence: 99%

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Units in $F(C_n \times Q_{12})$ and $F(C_n \times D_{12})$

Sahai

Ansari

2023

International Electronic Journal of Algebra

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Let $C_n$, $Q_n$ and $D_n$ be the cyclic group, the quaternion group and the dihedral group of order $n$, respectively. Recently, the structures of the unit groups of the finite group algebras of $2$-groups that contain a normal cyclic subgroup of index $2$ have been studied. The dihedral groups $D_{2n}, n\geq 3$ and the generalized quaternion groups $Q_{4n}, n\geq 2$ also contain a normal cyclic subgroup of index $2$. The structures of the unit groups of the finite group algebras $FQ_{12}$, $FD_{12}$, $F(C_2 \times Q_{12})$ and $F(C_2 \times D_{12})$ over a finite field $F$ are well known. In this article, we continue this investigation and establish the structures of the unit groups of the group algebras $F(C_n \times Q_{12})$ and $F(C_n \times D_{12})$ over a finite field $F$ of characteristic $p$ containing $p^k$ elements.

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Section: Introductionmentioning

confidence: 99%

“…The groups D 2n , n ≥ 3 and Q 4n , n ≥ 2 also contain a normal cyclic subgroup of index 2 and the unit groups of the group algebras of these groups and their extensions have been extensively studied [6,7,9,11,13,14,16,17,18,21,23,25,26]. In this paper, we aim to contribute in this direction further by describing the structures…”

Section: Introductionmentioning

confidence: 99%

Units in $F(C_n \times Q_{12})$ and $F(C_n \times D_{12})$

Sahai

Ansari

2023

International Electronic Journal of Algebra

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“…In the same paper, the structure of U (F Q 20 ) for the semisimple case is also given. In [18], they established the structure of the unit groups U (F Q 2 n ) of the finite group algebras of the generalized quaternion groups Q 2 n , p > 2.…”

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confidence: 99%