Yakov G. Berkovich - Characters of Finite Groups: Volume 2

Yakov G. Berkovich, Lev S. Kazarin, Emmanuel M. Zhmud

Characters of Finite Groups

De Gruyter Expositions in Mathematics

Edited by

Lev Birbrair, Universidade Federal do Cear, Fortaleza, Brazil
Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia
Walter D. Neumann, Columbia University, New York, USA
Markus J. Pflaum, University of Colorado, Boulder, USA
Dierk Schleicher, Jacobs University, Bremen, Germany
Katrin Wendland, University of Freiburg, Germany

Volume 64

Mathematics Subject Classification 2010

20C15

Authors

Prof. Dr. Yakov G. Berkovich

18251 Afula

Israel

Prof. Dr. Lev S. Kazarin

Yaroslavl P. Demidov State University

Department of Mathematics

Sovetskaya Str. 14

150000 Yaroslav

Russia

ISBN 978-3-11-022408-5

e-ISBN (PDF) 978-3-11-022409-2

e-ISBN (EPUB) 978-3-11-038480-2

ISSN 0938-6572

Library of Congress Control Number: 2018953197

Bibliographic information published by the Deutsche Nationalbibliothek

The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie;
detailed bibliographic data are available on the Internet at http://dnb.dnb.de.

2019 Walter de Gruyter GmbH, Berlin/Boston

www.degruyter.com

• |M| is the cardinality of a set (if is a group, then |G| is called the orderof ).
• xM means that is an element of . NM means that is a subset of; if NM, we write NM.
• is the empty set.
• is called a nontrivial subset of , if N and NM. If NM, we say that is a proper subset of .
• MN is the intersection and MN is the union of sets and . If M,Nare sets, then N-M is the difference of and .
• is the set (field) of complex numbers.
• is the set (field) of real numbers.
• is the set (field) of rational numbers.
• is the set (ring) of integers: Z={0,1,2,}.
• is the set of natural numbers.

• is always a prime number.
• m,n are always natural numbers.
• GCD(m,n) is the greatest common divisor of and .
• mn should be read as follows: divides .
• (m) is the set of all prime divisors of .
• is a set of primes (it may be the empty set).
• is the set of primes not contained in .
• m is the number satisfying the following three conditions:(m), mm, (m/m).
• We write mp, p instead of m{p},{p}, respectively.
• is a -number if (m) (or m=m).
• GF(pm) is the finite field containing pm elements.
• F* is the multiplicative group of a field .
• Fn is the -dimensional vector space over .
• Fn is the set of all nn matrices over .
• If is a square matrix, then detA and trA are the determinant and the traceof (that is, the sum of elements on its principal diagonal), respectively.
• In