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ZL-amenability Constants of Finite Groups with Two Character Degrees

Published online by Cambridge University Press:  20 November 2018

Mahmood Alaghmandan ,
Yemon Choi  and
Ebrahim Samei
Mahmood Alaghmandan
Affiliation:
Department of Mathematics and Statistics, McLean Hall, University of Saskatchewan, Saskatoon, SK S7N 5E6 e-mail: mahmood.a@usask.cachoi@math.usask.casamei@math.usask.ca
Yemon Choi
Affiliation:
Department of Mathematics and Statistics, McLean Hall, University of Saskatchewan, Saskatoon, SK S7N 5E6 e-mail: mahmood.a@usask.cachoi@math.usask.casamei@math.usask.ca
Ebrahim Samei
Affiliation:
Department of Mathematics and Statistics, McLean Hall, University of Saskatchewan, Saskatoon, SK S7N 5E6 e-mail: mahmood.a@usask.cachoi@math.usask.casamei@math.usask.ca
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Abstract

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We calculate the exact amenability constant of the centre of ${{\ell }^{1}}\left( G \right)$ when $G$ is a finite group and is either dihedral, extraspecial, or Frobenius with abelian complement and kernel. This is done using a formula that 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.

Keywords

43A2020C15center of group algebrascharacterscharacter degreesamenability constantFrobenius groupextraspecial groups
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 3 , 01 September 2014 , pp. 449 - 462
Copyright
Copyright © Canadian Mathematical Society 2014

References

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