Peer-Reviewed Journal Details
Mandatory Fields
Masterson, B,Pfeiffer, G
2018
April
Journal Of Algebra
On the table of marks of a direct product of finite groups
Published
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Optional Fields
Burnside ring Table of marks Subgroup lattice Double Burnside ring Ghost ring Mark homomorphism DOUBLE BURNSIDE RING FUSION SYSTEMS
499
610
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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.
10.1016/j.jalgebra.2017.12.019
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