On the Higman-Sims simple group of order 44,352,000

David L. Parrott and S. K. Wong

Vol. 32 (1970), No. 2, 501–516

DOI: 10.2140/pjm.1970.32.501

Abstract

In a recent paper D. G. Higman and C. C. Sims announced their construction of a new simple group H₁₀₀ of order 44,352,000. The group H₁₀₀ is obtained as a rank 3 permutation group of degree 100 with subdegrees 1,22 and 77; and the stabilizer of a point is isomorphic to the Mathieu simple group M₂₂. Shortly after their announcement of the new simple group, Graham Higman constructed a simple group of the same order as a doubly transitive group of degree 176 and with stabilizer of a point isomorphic to PSU(3,5²).

The purpose of this paper is to show that the two groups mentioned above are isomorphic, and in fact, that there is exactly one (up to isomorphism) simple group of order 44,352,000.

Mathematical Subject Classification

Primary: 20.29

Milestones

Received: 8 January 1969

Published: 1 February 1970