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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Item Type: | Article |
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Item Status: | Live Archive |

## 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):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 |
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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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