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ZL-amenability constants of finite groups with two character degrees. (English) Zbl 1300.43004
Summary: 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 A. Azimifard and N. Spronk [J. Funct. Anal. 256, No. 5, 1544–1564 (2009; Zbl 1167.43004)].

##### MSC:
 43A20 $$L^1$$-algebras on groups, semigroups, etc. 20C15 Ordinary representations and characters
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