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
Type | Article |
---|---|
Title | On the table of marks of a direct product of finite groups |
Authors | Masterson, 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. |
Keywords | Burnside ring; Table of marks; Subgroup lattice; Double Burnside ring; Ghost ring; Mark homomorphism |
Publisher | Elsevier |
Journal | Journal of Algebra |
ISSN | 0021-8693 |
Electronic | 1090-266X |
Publication dates | |
Online | 28 Dec 2017 |
01 Apr 2018 | |
Publication process dates | |
Deposited | 09 Jan 2018 |
Accepted | 28 Dec 2017 |
Submitted | 03 Jul 2017 |
Output status | Published |
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 identifier | WOS:000425578400028 |
Language | English |
https://repository.mdx.ac.uk/item/87650
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