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A Constructive Proof of Brauer's Theorem on Induced Characters in the Group Ring

Published online by Cambridge University Press:  18 December 2013

Fedor Bogomolov  and
Frederick P. Greenleaf
Fedor Bogomolov
Affiliation:
Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA ([email protected])
Frederick P. Greenleaf
Affiliation:
Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA ([email protected])
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Abstract

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We provide an alternative constructive proof of the classical Brauer theorem for finite groups based on the well-known description of the complex irreducible representations of the symmetric groups Sn. The theorem is first proved for Sn and then for general G by embedding in Sn and applying the Mackey subgroup theorem.

Keywords

Brauer theoremsymmetric groupslong cyclesinduced charactersYoung diagramsPrimary 20B3020C1520C30Secondary 06B15
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 57 , Issue 1 , February 2014 , pp. 31 - 53
Copyright
Copyright © Edinburgh Mathematical Society 2014 

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