Journal of the London Mathematical Society



WEAK CAYLEY TABLES


KENNETH W. JOHNSON a1 1 , SANDRO MATTAREI a2p1 and SURINDER K. SEHGAL a3
a1 Abington College, Pennsylvania State University, 1600 Woodland Road, Abington, PA 19001, USA; kwj1@psu.edu
a2 Dipartimento di Matematica Pura ed Applicata, via Belzoni 7, Università di Padova, I-35131 Padova, Italy; mattarei@math.unipd.it
a3 Department of Mathematics, Ohio State University, 231 W 18th Avenue, Columbus, Ohio 43210, USA; sehgal@math.ohio-state.edu

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) [rightward arrow] [open face C] 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].

(Received March 21 1997)
(Revised January 22 1999)


Correspondence:
p1 Current address: Dipartimento di Matematica, Università di Trento, I-38050 POVO (Trento), Italy; mattarei@science.unitn.it


Footnotes

1 The first author was partially supported by the Mathematical Research Institute at the Ohio State University.