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Izvestiya: Mathematics, 2012, Volume 76, Issue 6, Pages 1163–1174
DOI: https://doi.org/10.1070/IM2012v076n06ABEH002619
(Mi im7331)
 

This article is cited in 1 scientific paper (total in 1 paper)

Splitting fields of finite groups

D. D. Kiselev

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
References:
Abstract: We give a simpler proof of the Goldschmidt–Isaacs theorem in the case $p>2$ and find new sufficient conditions for the applicability of the theorem in the case $p=2$. We thus obtain a theorem giving an estimate for the Schur index of an arbitrary irreducible complex representation of a finite group over the field of rational numbers. The proof of this theorem shows that in practical applications there is no need to verify sufficient conditions for the applicability of the Goldschmidt–Isaacs theorem in the case $p=2$: they can automatically be assumed to hold. We also prove a theorem on the connection between the realizability of any complex representation over the field of rational numbers of a finite group of odd order of a special type and the possibility of constructing regular polygons with straightedge and compasses.
Keywords: finite group, representation of a finite group, Schur index.
Received: 01.03.2011
Revised: 18.05.2012
Bibliographic databases:
Document Type: Article
UDC: 512.547.2
MSC: 20C15, 12F10
Language: English
Original paper language: Russian
Citation: D. D. Kiselev, “Splitting fields of finite groups”, Izv. Math., 76:6 (2012), 1163–1174
Citation in format AMSBIB
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\by D.~D.~Kiselev
\paper Splitting fields of finite groups
\jour Izv. Math.
\yr 2012
\vol 76
\issue 6
\pages 1163--1174
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Linking options:
  • https://www.mathnet.ru/eng/im7331
  • https://doi.org/10.1070/IM2012v076n06ABEH002619
  • https://www.mathnet.ru/eng/im/v76/i6/p95
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
     
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