On the table of marks of a direct product of finite groups
Masterson, Brendan Pfeiffer, Götz
Masterson, Brendan
Pfeiffer, Götz
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http://hdl.handle.net/10379/14633
https://doi.org/10.13025/15319
https://doi.org/10.13025/15319
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Publication Date
2017-12-28
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Article
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Masterson, Brendan, & Pfeiffer, Götz. (2018). On the table of marks of a direct product of finite groups. Journal of Algebra, 499, 610-644. doi: https://doi.org/10.1016/j.jalgebra.2017.12.019
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. (C) 2017 Elsevier Inc. All rights reserved.
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Elsevier
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Attribution-NonCommercial-NoDerivs 3.0 Ireland