Let G be a finite p-group and let F be the field of p elements. It is shown that if G is elementary abelian-by-cyclic then the isomorphism type of G is determined by FG.
In this paper, we study the situation as to when the unit group U(KG) of a group algebra KG equals K*G(1 + J(KG)), where K is a field of characteristic p > 0 and G is a finite group.
Let be a semisimple complex algebraic group and its flag variety. Let and let be its enveloping algebra. Let be a Cartan subalgebra of . For , let be the corresponding minimal primitive ideal, let , and let be the Hattori-Stallings trace. Results of Hodges suggest to study this map as a step towards a classification, up to isomorphism or Morita equivalence, of the -algebras . When is regular, Hodges has shown that . In this case is generated by the classes corresponding to...
Let be a finite nonabelian group, its associated integral group ring, and its augmentation ideal. For the semidihedral group and another nonabelian 2-group the problem of their augmentation ideals and quotient groups is deal with. An explicit basis for the augmentation ideal is obtained, so that the structure of its quotient groups can be determined.
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, of a -adic analytic group . For without any -torsion element we prove that is an Auslander regular ring. This result enables us to give a good definition of the notion of a pseudo-null -module. This is classical when for some integer , but was previously unknown in the non-commutative case. Then the category of -modules...