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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the number of conjugacy class sizes and character degrees in finite $p$-groups


Authors: Gustavo A. Fernández-Alcober and Alexander Moretó
Journal: Proc. Amer. Math. Soc. 129 (2001), 3201-3204
MSC (1991): Primary 20C15, 20D15
Published electronically: March 29, 2001
MathSciNet review: 1844993
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Abstract:

In this note we prove that for any two integers $r,s>1$ there exist finite $p$-groups $G$ of class $2$ such that $\vert\operatorname{cd}(G)\vert=r$ and $\vert\operatorname{cs}(G)\vert=s$.


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Additional Information

Gustavo A. Fernández-Alcober
Affiliation: Departamento de Matemáticas, Universidad del País Vasco, 48080 Bilbao, Spain
Email: mtpfealg@lg.ehu.es

Alexander Moretó
Affiliation: Departamento de Matemáticas, Universidad del País Vasco, 48080 Bilbao, Spain
Email: mtbmoqua@lg.ehu.es

DOI: http://dx.doi.org/10.1090/S0002-9939-01-05946-9
PII: S 0002-9939(01)05946-9
Received by editor(s): February 14, 2000
Received by editor(s) in revised form: March 31, 2000
Published electronically: March 29, 2001
Additional Notes: Research of the second author was supported by a grant of the Basque Government and by the University of the Basque Country grant UPV 127.310-EB160/98.
Communicated by: Stephen D. Smith
Article copyright: © Copyright 2001 American Mathematical Society