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

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Journal publication date 2014 Canadian Mathematical Bulletin 57 14 449-462 Published 19/07/13 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).