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WEAK CAYLEY TABLES

Published online by Cambridge University Press:  01 April 2000

KENNETH W. JOHNSON ,
SANDRO MATTAREI  and
SURINDER K. SEHGAL
KENNETH W. JOHNSON
Affiliation:
Abington College, Pennsylvania State University, 1600 Woodland Road, Abington, PA 19001, USA; kwj1@psu.edu
SANDRO MATTAREI
Affiliation:
Dipartimento di Matematica Pura ed Applicata, via Belzoni 7, Università di Padova, I-35131 Padova, Italy; mattarei@math.unipd.it Current address: Dipartimento di Matematica, Università di Trento, I-38050 POVO (Trento), Italy; mattarei@science.unitn.it
SURINDER K. SEHGAL
Affiliation:
Department of Mathematics, Ohio State University, 231 W 18th Avenue, Columbus, Ohio 43210, USA; sehgal@math.ohio-state.edu
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Abstract

In [1] Brauer puts forward a series of questions on group representation theory in order to point out areas which were not well understood. One of these, which we denote by (B1), is the following: what information in addition to the character table determines a (finite) group? In previous papers [5, 7–13], the original work of Frobenius on group characters has been re-examined and has shed light on some of Brauer's questions, in particular an answer to (B1) has been given as follows.

Frobenius defined for each character χ of a group G functions χ(k)[ratio ]G(k) → [Copf ] for k = 1, …, degχ with χ(1) = χ. These functions are called the k-characters (see [10] or [11] for their definition). The 1-, 2- and 3-characters of the irreducible representations determine a group [7, 8] but the 1- and 2-characters do not [12]. Summaries of this work are given in [11] and [13].

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 61 , Issue 2 , April 2000 , pp. 395 - 411
Copyright
The London Mathematical Society 2000

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