On the table of marks of a direct product of finite groups

Article


Masterson, B. and Pfeiffer, G. 2018. On the table of marks of a direct product of finite groups. Journal of Algebra. 499, pp. 610-644. https://doi.org/10.1016/j.jalgebra.2017.12.019
TypeArticle
TitleOn the table of marks of a direct product of finite groups
AuthorsMasterson, B. and Pfeiffer, G.
Abstract

We present a method for computing the table of marks of a direct product of finite groups. In contrast to the character table of a direct product of two finite groups, its table of marks is not simply the Kronecker product of the tables of marks of the two groups. Based on a decomposition of the inclusion order on the subgroup lattice of a direct product as a relation product of three smaller partial orders, we describe the table of marks of the direct product essentially as a matrix product of three class incidence matrices. Each of these matrices is in turn described as a sparse block diagonal matrix. As an application, we use a variant of this matrix product to construct a ghost ring and a mark homomorphism for the rational double Burnside algebra of the symmetric group S_3.

KeywordsBurnside ring; Table of marks; Subgroup lattice; Double Burnside ring; Ghost ring; Mark homomorphism
LanguageEnglish
PublisherElsevier
JournalJournal of Algebra
ISSN0021-8693
Electronic1090-266X
Publication dates
Online28 Dec 2017
Print01 Apr 2018
Publication process dates
Deposited09 Jan 2018
Accepted28 Dec 2017
Submitted03 Jul 2017
Output statusPublished
Accepted author manuscript
License
Copyright Statement

© 2017. This author's accepted manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

Digital Object Identifier (DOI)https://doi.org/10.1016/j.jalgebra.2017.12.019
Web of Science identifierWOS:000425578400028
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