Class Group Relations from Burnside Ring Idempotents

The slice Burnside ring and the section Burnside ring of a finite group

This paper introduces two new Burnside rings for a finite group G, called the slice Burnside ring and the section Burnside ring. They are built as Grothendieck rings of the category of morphisms of G-sets, and of Galois morphisms of G-sets, respectively. The well known results on the usual Burnside ring, concerning ghost maps, primitive idempotents, and description of the prime spectrum, are ex...

Smarandache Idempotents in finite ring Zn and in Group Ring ZnG

In this paper we analyze and study the Smarandache idempotents (S-idempotents) in the ring Zn and in the group ring ZnG of a finite group G over the finite ring Zn. We have shown the existance of Smarandache idempotents (S-idempotents) in the ring Zn when n = 2 p (or 3p), where p is a prime > 2 (or p a prime > 3). Also we have shown the existance of Smarandache idempotents (S-idempotents) in th...

An Algorithm for the Unit Group of the Burnside Ring of a Finite Group

In this note we present an algorithm for the construction of the unit group of the Burnside ring Ω(G) of a finite group G from a list of representatives of the conjugacy classes of subgroups of G.

Idempotents in Group Algebras

In this survey we collect and present the classical and some recent methods to compute the primitive (central) idempotents in semisimple group algebras. MSC 2010. 20C05, 20C15, 16S34, 16U60.

Central Idempotents in Group Algebras