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Representation of Groups by Generalized Normal Multiplication Tables

Published online by Cambridge University Press:  20 November 2018

A. Ginzburg
A. Ginzburg*
Affiliation:
Carnegie Institute of Technology, Pittsburgh, Pennsylvania, U.S.A.
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G will denote a finite (or infinite) group of order n. In a normal multiplication table (n.m.t.) of G (7, 8, 9, 12) all entries in one diagonal are equal to e (the identity of G), and if the entry on the intersection of the ith column and jth row is gi,j ∈ G, then

The following is a n.m.t. of Z6 = {0, 1, 2, 3, 4, 5}:

Remark. The cyclic groups Zn will always be written in additive notation. The table is uniquely defined by every one of its columns, in particular by the first.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 774 - 791
Copyright
Copyright © Canadian Mathematical Society 1967

References

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