Groups Generated by a Class of Elements of Order 3,
Abstract
The Conway group which is the group of automorphisms of the 24 dimensional Leech lattice is generated by a class of elements of order 3 with the property that any two of them either commute or generate SL2(3), SL2(5) or the alternating groups A4, A5 which are isomorphic to SL2(3) and SL2(5) modulo a center of order 2. Such a class of order 3 is also a special case of John Thompson's Quadratic pairs for the prime 3. The paper is restricted to elements of order 3 in which any two either commute, generate A4 or SL2(3). It is possible to describe these groups completely. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1970
- Accession Number
- AD0736220
Entities
People
- Marshall Hall Jr.
- Michael Aschbacher
Organizations
- California Institute of Technology