Conjugacy classes and characters of finite p-groups

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autoren

  • Lászlo Héthelyi
  • Burkhard Külshammer
  • Benjamin Sambale

Externe Organisationen

  • Budapest University of Technology and Economics
  • Friedrich-Schiller-Universität Jena
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Seiten (von - bis)657-685
Seitenumfang29
FachzeitschriftCommunications in algebra
Jahrgang39
Ausgabenummer2
PublikationsstatusVeröffentlicht - Feb. 2011
Extern publiziertJa

Abstract

Let K be a conjugacy class of a finite p-group G where p is a prime, and let K-1 denote the conjugacy class of G consisting of the inverses of the elements in K. We observe that, in several cases, the number of elements in the product KK-1 is congruent to 1 modulo p -1, and we pose the question in which generality this congruence is valid. We also consider related properties of the class multiplication constants of G. Furthermore, let χ be an irreducible character of G, and let χ- denote the complex conjugate of χ. We show that, in several cases, the number of irreducible constituents of the product χχ- is congruent to 1 modulo p -1, and we pose the question in which generality this congruence is valid.

ASJC Scopus Sachgebiete

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Conjugacy classes and characters of finite p-groups. / Héthelyi, Lászlo; Külshammer, Burkhard; Sambale, Benjamin.
in: Communications in algebra, Jahrgang 39, Nr. 2, 02.2011, S. 657-685.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Héthelyi, L, Külshammer, B & Sambale, B 2011, 'Conjugacy classes and characters of finite p-groups', Communications in algebra, Jg. 39, Nr. 2, S. 657-685. https://doi.org/10.1080/00927871003598723
Héthelyi L, Külshammer B, Sambale B. Conjugacy classes and characters of finite p-groups. Communications in algebra. 2011 Feb;39(2):657-685. doi: 10.1080/00927871003598723
Héthelyi, Lászlo ; Külshammer, Burkhard ; Sambale, Benjamin. / Conjugacy classes and characters of finite p-groups. in: Communications in algebra. 2011 ; Jahrgang 39, Nr. 2. S. 657-685.
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AU - Külshammer, Burkhard

AU - Sambale, Benjamin

N1 - Funding Information: The authors are grateful to J. Schmidt [14] for providing GAP files containing the groups of order 37 and 57. Also, the first named author was supported by an OTKA grant (National Scientific Research Grant No. T049841).

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