Conjugacy classes and characters of finite p-groups

Research output: Contribution to journal › Article › Research › peer review

Authors

  • Lászlo Héthelyi
  • Burkhard Külshammer
  • Benjamin Sambale

External Research Organisations

  • Budapest University of Technology and Economics
  • Friedrich Schiller University Jena
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Details

Original languageEnglish
Pages (from-to)657-685
Number of pages29
JournalCommunications in algebra
Volume39
Issue number2
Publication statusPublished - Feb 2011
Externally publishedYes

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.

Keywords

    Character, Conjugacy class

ASJC Scopus subject areas

Cite this

Conjugacy classes and characters of finite p-groups. / Héthelyi, Lászlo; Külshammer, Burkhard; Sambale, Benjamin.
In: Communications in algebra, Vol. 39, No. 2, 02.2011, p. 657-685.

Research output: Contribution to journal › Article › Research › peer review

Héthelyi, L, Külshammer, B & Sambale, B 2011, 'Conjugacy classes and characters of finite p-groups', Communications in algebra, vol. 39, no. 2, pp. 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 ; Vol. 39, No. 2. pp. 657-685.
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