Geodesic
ZL-amenability Constants of Finite Groups with Two Character Degrees
Canadian mathematical bulletin, Tome 57 (2014) no. 3, pp. 449-462

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-2013-022-1
Mots-clés : 43A20, 20C15, center of group algebras, characters, character degrees, amenability constant, Frobenius group, extraspecial groups 
Alaghmandan, Mahmood; Choi, Yemon; Samei, Ebrahim. ZL-amenability Constants of Finite Groups with Two Character Degrees. Canadian mathematical bulletin, Tome 57 (2014) no. 3, pp. 449-462. doi: 10.4153/CMB-2013-022-1
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[1] [1] Azimifard, A., Samei, E., and Spronk, N., Amenability properties of the centres of group algebras. J. Funct. Anal. 256 (2009), no. 5, 1544–1564. Google Scholar | DOI

[2] [2] Diaconis, P., Threads through group theory. In: Character theory of finite groups, Contemp. Math., 524, American Mathematical Society, Providence, RI, 2010, pp. 33–47. Google Scholar

[3] [3] Gorenstein, D., Finite groups. Second ed., Chelsea Publishing Co., New York, 1980. Google Scholar

[4] [4] Isaacs, I. M., Character theory of finite groups. Pure and Applied Mathematics, 69, Academic Press [Harcourt Brace Jovanovich Publishers], New York-London, 1976. Google Scholar

[5] [5] Isaacs, I. M. and Passman, D. S., A characterization of groups in terms of the degrees of their characters. II. Pacific J. Math. 24 (1968), 467–510. Google Scholar | DOI

[6] [6] James, G. and Liebeck, M., Representations and characters of groups. Second ed., Cambridge University Press, New York, 2001. Google Scholar

[7] [7] Passman, D., Permutation groups. W. A. Benjamin, Inc., New York-Amsterdam, 1968. Google Scholar

[8] [8] Rider, D., Central idempotent measures on compact groups. Trans. Amer. Math. Soc., 186 (1973), 459–479. Google Scholar | DOI

[9] [9] Stegmeir, U., Centers of group algebras. Math. Ann. 243 (1979), 11–16. Google Scholar | DOI

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