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ZL-amenability Constants of Finite Groups with Two Character Degrees

  • Mahmood Alaghmandan,
    Department of Mathematics and Statistics, McLean Hall, University of Saskatchewan, Saskatoon, SK S7N 5E6
  • Yemon Choi,
    Department of Mathematics and Statistics, McLean Hall, University of Saskatchewan, Saskatoon, SK S7N 5E6
  • Ebrahim Samei,
    Department of Mathematics and Statistics, McLean Hall, University of Saskatchewan, Saskatoon, SK S7N 5E6
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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).
Keywords: center of group algebras, characters, character degrees, amenability constant, Frobenius group, extraspecial groups center of group algebras, characters, character degrees, amenability constant, Frobenius group, extraspecial groups
MSC Classifications: 43A20, 20C15 show english descriptions $L^1$-algebras on groups, semigroups, etc.
Ordinary representations and characters
43A20 - $L^1$-algebras on groups, semigroups, etc.
20C15 - Ordinary representations and characters
 

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