Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

A natural invariant algebra for the Harada-Norton group

A. J. E. Rybaa1

a1 Department of Mathematics, Statistics and Computer Science, Marquette University, Milwaukee, WI 53233, U.S.A.

The Harada-Norton group is one of the twenty-six sporadic simple groups. It has order 273, 030, 912, 000, 000 = 214.36.56.7.11.19. In this paper our main objective is:

Theorem 1. The Harada-Norton group acts as a group of linear automorphisms of a 133-dimensional commutative, non-associative algebra defined over F5.

(Received July 05 1993)

(Revised April 19 1995)