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ZL-amenability constants of finite groups with two character degrees

Authors

Mahmood Alaghmandan, Yemon Choi*, Ebrahim Samei

* Corresponding author

Metadata

Keywords: center of group algebras, characters, character degrees, amenability constant, Frobenius group, extraspecial groups

MSC 2010: 43A20 (primary), 20C15 (secondary)

DOI: 10.4153/CMB-2013-022-1

Status

Appeared as Canadian Math. Bull. 57 (2014), no. 3, 449–462

Preprint version available at arXiv 1302.1929

Reviews

[ Math Review (summary) | Zentralblatt (summary) ]

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).

Note added in proof

After this paper was accepted for publication, the second author (YC) has since shown that the ZL-amenability constant of any finite non-abelian group is at least 7/4. Details will appear in a forthcoming work.

Updates/comments

This article uses material from the unpublished preprint 1110.6863v1, which was later split up into two separate papers (of which this is one).

For the "forthcoming work" mentioned above, see this paper.


Yemon Choi

Last updated 25th October 2014.