## ZL-amenability constants of finite groups with two character degrees

#### Authors

Mahmood Alaghmandan, Yemon Choi*, Ebrahim Samei

* Corresponding author

Keywords: center of group algebras, characters, character degrees, amenability constant, Frobenius group, extraspecial groups

MSC 2010: 43A20 (primary), 20C15 (secondary)

DOI: 10.4153/CMB-2013-022-1

#### Status

Preprint version available at arXiv 1302.1929

#### Abstract

We calculate the exact amenability constant of the centre of $\ell^1(G)$ when $G$ 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).