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On the derived length of units in group algebra

Dishari Chaudhuri, Anupam Saikia (2017)

Czechoslovak Mathematical Journal

Let G be a finite group G , K a field of characteristic p 17 and let U be the group of units in K G . We show that if the derived length of U does not exceed 4 , then G must be abelian.

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

Jizhu Nan, Huifang Zhao (2012)

Czechoslovak Mathematical Journal

Let G be a finite nonabelian group, 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.

On the structure theory of the Iwasawa algebra of a p-adic Lie group

Otmar Venjakob (2002)

Journal of the European Mathematical Society

This paper is motivated by the question whether there is a nice structure theory of finitely generated modules over the Iwasawa algebra, i.e. the completed group algebra, Λ of a p -adic analytic group G . For G without any p -torsion element we prove that Λ is an Auslander regular ring. This result enables us to give a good definition of the notion of a pseudo-null Λ -module. This is classical when G = p k for some integer k 1 , but was previously unknown in the non-commutative case. Then the category of Λ -modules...

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