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# ZL-amenability Constants of Finite Groups with Two Character Degrees

Published:2013-07-19
Printed: Sep 2014
• 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
 Format: LaTeX MathJax PDF

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

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