Accession Number : AD0736220

Title :   Groups Generated by a Class of Elements of Order 3,

Corporate Author : CALIFORNIA INST OF TECH PASADENA DEPT OF MATHEMATICS

Personal Author(s) : Aschbacher,Michael ; Hall,Marshall , Jr

Report Date : 1970

Pagination or Media Count : 41

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)

Descriptors :   (*GROUPS(MATHEMATICS), THEOREMS), SET THEORY, ALGEBRA, COMBINATORIAL ANALYSIS, PERMUTATIONS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE