On a theorem of Blichfeldt

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

Authors

  • Benjamin Sambale

External Research Organisations

  • University of Kaiserslautern
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Details

Original languageEnglish
Pages (from-to)221-225
Number of pages5
JournalExpositiones mathematicae
Volume35
Issue number2
Publication statusPublished - Jun 2017
Externally publishedYes

Abstract

Let G be a permutation group on n<∞ objects. Let f(g) be the number of fixed points of g∈G, and let {f(g):1≠g∈G}={f1,…,fr}. In this expository note we give a character-free proof of a theorem of Blichfeldt which asserts that the order of G divides (n−f1)…(n−fr). We also discuss the sharpness of this bound.

Keywords

    Blichfeldt's theorem, Number of fixed points, Permutation character

ASJC Scopus subject areas

Cite this

On a theorem of Blichfeldt. / Sambale, Benjamin.
In: Expositiones mathematicae, Vol. 35, No. 2, 06.2017, p. 221-225.

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

Sambale B. On a theorem of Blichfeldt. Expositiones mathematicae. 2017 Jun;35(2):221-225. doi: 10.1016/j.exmath.2016.10.002
Sambale, Benjamin. / On a theorem of Blichfeldt. In: Expositiones mathematicae. 2017 ; Vol. 35, No. 2. pp. 221-225.
Download
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