ZL-amenability constants of finite groups with two character degrees

Alaghmandan, Mahmood and Choi, Yemon and Samei, Ebrahim (2014) ZL-amenability constants of finite groups with two character degrees. Canadian Mathematical Bulletin, 57. pp. 449-462. ISSN 0008-4395

Abstract

We calculate the exact amenability constant of the centre of $\ell^1(G)$ when is one of the following classes of finite group: dihedral; extraspecial; or Frobenius with abelian complement and kernel. This is done using a formula which 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 (J. Funct. Anal. 2009).