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Weak Cayley Tables
Author(s) -
Johnson Kenneth W.,
Mattarei Sandro,
Sehgal Surinder K.
Publication year - 2000
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610799008571
Subject(s) - character table , character (mathematics) , group (periodic table) , mathematics , finite group , order (exchange) , brauer's theorem on induced characters , combinatorics , point (geometry) , table (database) , representation (politics) , pure mathematics , algebra over a field , brauer group , computer science , physics , geometry , finance , quantum mechanics , politics , law , political science , economics , data mining
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 ].