The structure of the unit group of the group algebra $\mathbb {F}_{2^k}A_4$

Joe Gildea

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Unit groups of group algebras of some small groups

Gaohua Tang, Yangjiang Wei, Yuanlin Li (2014)

Czechoslovak Mathematical Journal

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Let $F G$ be a group algebra of a group $G$ over a field $F$ and $𝒰 (F G)$ the unit group of $F G$ . It is a classical question to determine the structure of the unit group of the group algebra of a finite group over a finite field. In this article, the structure of the unit group of the group algebra of the non-abelian group $G$ with order $21$ over any finite field of characteristic $3$ is established. We also characterize the structure of the unit group of $F A_{4}$ over any finite field of characteristic $3$ and the...

$G$ -nilpotent units of commutative group rings

Peter Vassilev Danchev (2012)

Commentationes Mathematicae Universitatis Carolinae

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Suppose $R$ is a commutative unital ring and $G$ is an abelian group. We give a general criterion only in terms of $R$ and $G$ when all normalized units in the commutative group ring $R G$ are $G$ -nilpotent. This extends recent results published in [Extracta Math., 2008–2009] and [Ann. Sci. Math. Québec, 2009].

On the structure of the augmentation quotient group for some nonabelian 2-groups

Jizhu Nan, Huifang Zhao (2012)

Czechoslovak Mathematical Journal

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Let $G$ be a finite nonabelian group, $ℤ G$ its associated integral group ring, and $▵ (G)$ its augmentation ideal. For the semidihedral group and another nonabelian 2-group the problem of their augmentation ideals and quotient groups $Q_{n} (G) = ▵^{n} (G) / ▵^{n + 1} (G)$ is deal with. An explicit basis for the augmentation ideal is obtained, so that the structure of its quotient groups can be determined.

Displaying similar documents to “The structure of the unit group of the group algebra 𝔽 2 k A 4 ”

Unit groups of group algebras of some small groups

G -nilpotent units of commutative group rings

On the structure of the augmentation quotient group for some nonabelian 2-groups

Displaying similar documents to “The structure of the unit group of the group algebra $𝔽_{2^{k}} A_{4}$ ”

$G$ -nilpotent units of commutative group rings