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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

[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. http://dx.doi.org/10.1016/j.jfa.2008.11.026 Google Scholar
[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] Gorenstein, D., Finite groups. Second ed., Chelsea Publishing Co., New York, 1980.Google Scholar
[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] 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. http://dx.doi.org/10.2140/pjm.1968.24.467 Google Scholar
[6] James, G. and Liebeck, M., Representations and characters of groups. Second ed., Cambridge University Press, New York, 2001.Google Scholar
[7] Passman, D., Permutation groups. W. A. Benjamin, Inc., New York-Amsterdam, 1968.Google Scholar
[8] Rider, D., Central idempotent measures on compact groups. Trans. Amer. Math. Soc., 186 (1973), 459–479. http://dx.doi.org/10.1090/S0002-9947-1973-0340961-0 Google Scholar
[9] Stegmeir, U., Centers of group algebras. Math. Ann. 243 (1979), 11–16. http://dx.doi.org/10.1007/BF01420202 Google Scholar