ZL-amenability constants of finite groups with two character degrees

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).

To appear in Canadian Mathematical Bulletin, 14 pages. Uses material from an older, unpublished preprint http://arxiv.org/abs/1110.6683v1 which has since been superseded. v3: Correction of some grant details and a few minor (non-mathematical) adjustments; note added at page proof stages to reflect new developments

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