The Terwilliger algebras of the group association schemes of non-abelian finite groups admitting an abelian subgroup of index 2

TL;DR

This paper investigates the structure of Terwilliger algebras for certain non-abelian finite groups with an abelian subgroup of index 2, revealing their triply transitive nature and detailing their Wedderburn components.

Contribution

It provides a complete characterization of the Terwilliger algebras for these groups and determines their dimensions, advancing understanding of their algebraic structure.

Findings

Terwilliger algebras are triply transitive for these groups

Explicit description of Wedderburn components

Dimension formulas for the Terwilliger algebras

Abstract

In this paper, we determine the dimension of the Terwilliger algebras of non-abelian finite groups admitting an abelian subgroup of index 2 by showing that they are triply transitive. Moreover, we give a complete characterization of the Wedderburn components of the Terwilliger algebras of these groups.