Optimal bounds for the Schur index and the realizability of representations

doi:10.1070/SM2014V205N04ABEH004386

Title: Optimal bounds for the Schur index and the realizability of representations

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Abstract

An optimal bound is given for the Schur index of an irreducible complex representation over the field of rational numbers on the class of finite groups of a chosen order or of a chosen exponent. We obtain a sufficient condition for the realizability of an irreducible complex character χ of a finite group G of exponent n with Schur index m, which is either an odd number or has 2-part no smaller than 4, over the field of rational numbers in a field L which is a subfield of Q({sup n}√1 ) and (L:Q(χ))=m. This condition generalizes the well-known Fein condition obtained by him in the case of n=p{sup α}q{sup β}. The formulation of the Grunwald-Wang problem on the realizability of representations is generalized, and some sufficient conditions are obtained. Bibliography: 10 titles. (paper)

Authors:

Kiselev, D. D., E-mail: denmexmath@yandex.ru ^[1]

Faculty of Mechanics and Mathematics, Moscow State University (Russian Federation)

Publication Date:: Wed Apr 30 00:00:00 EDT 2014

OSTI Identifier:: 22365291

Resource Type:: Journal Article

Journal Name:: Sbornik. Mathematics

Additional Journal Information:: Journal Volume: 205; Journal Issue: 4; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1064-5616

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICAL METHODS AND COMPUTING; COMPLEXES; GROUP THEORY; INDEXES; IRREDUCIBLE REPRESENTATIONS; MATHEMATICAL SOLUTIONS; SYMMETRY GROUPS

Citation Formats


                    Kiselev, D. D., E-mail: denmexmath@yandex.ru. Optimal bounds for the Schur index and the realizability of representations.  United States: N. p., 2014. 
        Web.  doi:10.1070/SM2014V205N04ABEH004386.

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                    Kiselev, D. D., E-mail: denmexmath@yandex.ru. Optimal bounds for the Schur index and the realizability of representations.  United States.  https://doi.org/10.1070/SM2014V205N04ABEH004386

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                    Kiselev, D. D., E-mail: denmexmath@yandex.ru. 2014.  
        "Optimal bounds for the Schur index and the realizability of representations".  United States.  https://doi.org/10.1070/SM2014V205N04ABEH004386.

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@article{osti_22365291,

  title        = {Optimal bounds for the Schur index and the realizability of representations},

  author       = {Kiselev, D. D., E-mail: denmexmath@yandex.ru},

  abstractNote = {An optimal bound is given for the Schur index of an irreducible complex representation over the field of rational numbers on the class of finite groups of a chosen order or of a chosen exponent. We obtain a sufficient condition for the realizability of an irreducible complex character χ of a finite group G of exponent n with Schur index m, which is either an odd number or has 2-part no smaller than 4, over the field of rational numbers in a field L which is a subfield of Q({sup n}√1 ) and (L:Q(χ))=m. This condition generalizes the well-known Fein condition obtained by him in the case of n=p{sup α}q{sup β}. The formulation of the Grunwald-Wang problem on the realizability of representations is generalized, and some sufficient conditions are obtained. Bibliography: 10 titles. (paper)},

  doi          = {10.1070/SM2014V205N04ABEH004386},

  url          = {https://www.osti.gov/biblio/22365291},
  journal      = {Sbornik. Mathematics},

  issn         = {1064-5616},

  number       = 4,

  volume       = 205,

  place        = {United States},

  year         = {Wed Apr 30 00:00:00 EDT 2014},

  month        = {Wed Apr 30 00:00:00 EDT 2014}

}

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