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On the invariants of a linear group of order 336

Published online by Cambridge University Press:  24 October 2008

C. L. Mallows  and
N. J. A. Sloane
C. L. Mallows
Affiliation:
Bell Laboratories, Murray Hill, New Jersey
N. J. A. Sloane
Affiliation:
Bell Laboratories, Murray Hill, New Jersey
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Abstract

The polynomial invariants of a certain classical linear group of order 336 arise naturally in studying error-correcting codes over GF(7). An incomplete description of these invariants was given by Maschke in 1893. With the aid of the Poincaré series for this group, found by Edge in 1947, we complete Maschke's work by giving a unique representation for the invariants in terms of 12 basic invariants. A conjecture is made concerning the relationship between the Poincaré series and the degrees of the basic invariants for any linear group. A partial answer to this conjecture, due to E. C. Dade, is given.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 74 , Issue 3 , November 1973 , pp. 435 - 440
Copyright
Copyright © Cambridge Philosophical Society 1973

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