skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

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

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:
 [1]
  1. Faculty of Mechanics and Mathematics, Moscow State University (Russian Federation)
Publication Date:
OSTI Identifier:
22365291
Resource Type:
Journal Article
Resource Relation:
Journal Name: Sbornik. Mathematics; Journal Volume: 205; Journal Issue: 4; Other Information: Country of input: International Atomic Energy Agency (IAEA)
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.
Kiselev, D. D., E-mail: denmexmath@yandex.ru. Optimal bounds for the Schur index and the realizability of representations. United States. doi:10.1070/SM2014V205N04ABEH004386.
Kiselev, D. D., E-mail: denmexmath@yandex.ru. Wed . "Optimal bounds for the Schur index and the realizability of representations". United States. doi:10.1070/SM2014V205N04ABEH004386.
@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},
journal = {Sbornik. Mathematics},
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}
}