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

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.