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ZL-amenability constants of finite groups with two character degrees

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<mark>Journal publication date</mark>2014
<mark>Journal</mark>Canadian Mathematical Bulletin
Volume57
Number of pages14
Pages (from-to)449-462
Publication StatusPublished
Early online date19/07/13
<mark>Original language</mark>English

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).