Computational aspects of Burnside rings, part I: the ring structure

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Abstract

The Burnside ring \(\mathcal {B}(G)\) of a finite group G, a classical tool in group theory and representation theory, is studied from the point of view of computational commutative algebra. Starting from a table of marks, we describe efficient algorithms for computing a presentation, the image of the mark homomorphism, the prime ideals and the prime ideal graph, the singular locus, the conductor in its integral closure, the connected components of its spectrum, and its idempotents. On the way, we provide methods for identifying p-residual subgroups, direct products of subgroups of coprime order, commutator subgroups, and perfect subgroups.

Keywords

Burnside ring Table of marks Prime ideal graph Spectrum Connected component Quasi-idempotent Idempotent 

Mathematics Subject Classification

Primary 19A22 Secondary 13F99 13P99 20C40 

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Copyright information

© The Managing Editors 2016

Authors and Affiliations

  1. 1.Fakultät für Informatik und MathematikUniversität PassauPassauGermany
  2. 2.Department of Mathematics/CSAIndian Institute of ScienceBangaloreIndia

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