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Mat. Sb., 2013, Volume 204, Number 8, Pages 73–82 (Mi msb8175)  

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

A bound for the Schur index of irreducible representations of finite groups

D. D. Kiselev

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We construct an optimal bound for the Schur index of irreducible complex representations of finite groups over the field of rational numbers, when only the prime divisors of the order of the group are known. We study relationships with compatible and universally compatible extensions of number fields. We give a simpler proof of the well-known Berman-Yamada bound for the Schur index over the field $\mathbb{Q}_p$.
Bibliography: 7 titles.

Keywords: finite group, Schur index, universally compatible extensions.

DOI: https://doi.org/10.4213/sm8175

Full text: PDF file (468 kB)
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English version:
Sbornik: Mathematics, 2013, 204:8, 1152–1160

Bibliographic databases:

UDC: 512.547.2+512.623.32
MSC: Primary 20C05; Secondary 20C99
Received: 12.09.2012 and 25.12.2012

Citation: D. D. Kiselev, “A bound for the Schur index of irreducible representations of finite groups”, Mat. Sb., 204:8 (2013), 73–82; Sb. Math., 204:8 (2013), 1152–1160

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/msb8175
  • https://doi.org/10.4213/sm8175
  • http://mi.mathnet.ru/eng/msb/v204/i8/p73

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. D. D. Kiselev, “Optimal bounds for the Schur index and the realizability of representations”, Sb. Math., 205:4 (2014), 522–531  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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