Weak Cayley tables

Johnson, Kenneth W. and Mattarei, Sandro and Sehgal, Surinder K. (2000) Weak Cayley tables. Journal of the London Mathematical Society, 61 (2). pp. 395-411. ISSN 0024-6107

Full content URL: http://dx.doi.org/10.1112/S0024610799008571

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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):G(k) → 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].

Keywords:Weak Cayley tables, Group representation theory
Subjects:G Mathematical and Computer Sciences > G100 Mathematics
Divisions:College of Science > School of Mathematics and Physics
ID Code:18518
Deposited On:17 Feb 2017 09:18

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