ZL-amenability Constants of Finite Groups with Two Character Degrees. Issue 3 (1st September 2014)

• Record Type: Journal Article
• Authors: Alaghmandan, Mahmood; Choi, Yemon; Samei, Ebrahim
• Is Part Of: Canadian mathematical bulletin =. Volume 57:Issue 3(2014)
• Page Start: 449
• Page End: 462
• Publication Date: 2014-09-01
• Subjects: 43A20 -- 20C15; center of group algebras -- characters -- character degrees -- amenability constant -- Frobenius group -- extraspecial groups; Mathematics -- Periodicals; Mathematics; Periodicals; 510.5
• DOI: 10.4153/CMB-2013-022-1
• Languages: English
• ISSNs: 0008-4395

Abstract

Abstract: 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.