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

Kreuzer, Martin and Patil, Dilip P (2017) Computational aspects of Burnside rings, part I: the ring structure. In: Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 58 (3). pp. 427-452. ISSN 0138-4821

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Abstract

The Burnside ring 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.

Item Type:	Journal Article
Publication:	Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
Publisher:	Springer Verlag
Additional Information:	The Copyright for this article belongs to the Springer Verlag.
Keywords:	Burnside ring; Connected component; Idempotent; Prime ideal graph; Quasi-idempotent; Spectrum; Table of marks
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	29 May 2022 07:36
Last Modified:	29 May 2022 07:36
URI:	https://eprints.iisc.ac.in/id/eprint/72767

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