ZL-amenability Constants of Finite Groups with Two Character Degrees

Abstract

AbstractWe calculate the exact amenability constant of the centre of ℓ1(G) when G is a finite group and is either dihedral, extraspecial, or Frobenius with abelian complement and kernel. This is done using a formula that applies to all finite groups with two character degrees. In passing, we answer in the negative a question raised in work of the third author with Azimifard and Spronk.