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- Title
The Terwilliger algebras of the group association schemes of three metacyclic groups.
- Authors
Yang, Jing; Zhang, Xiaoqian; Feng, Lihua
- Abstract
For any finite group G, the Terwilliger algebra T(G) of the group association scheme satisfies the following inclusions: T0(G)⊆T(G)⊆T˜(G), where T0(G) is a specific vector space and T˜(G) is the centralizer algebra of the permutation representation of G induced by the action of conjugation. The group G is said to be triply transitive if T0(G)=T˜(G). In this paper, we determine the dimensions of T0(G) and T˜(G) for G being Tn,k=〈a,b∣a2n=1,an=b2,bab−1=ak〉, Cn⋊Cp and Cp⋊Cn, and show that Tn,k,Cn⋊C2 and C3⋊C2n are triply transitive. Additionally, we give a complete characterization of the Wedderburn components of the Terwilliger algebras of Tn,k, Cn⋊Cp and Cp⋊Cn when they are triply transitive.
- Subjects
GROUP algebras; REPRESENTATIONS of algebras; FINITE groups; ALGEBRA; PERMUTATION groups
- Publication
Journal of Combinatorial Designs, 2024, Vol 32, Issue 8, p438
- ISSN
1063-8539
- Publication type
Article
- DOI
10.1002/jcd.21941