Radical 2-subgroups of the Monster and the Baby Monster

Congruence Subgroups Associated to the Monster

A Geometric Characterization of Fischer's Baby Monster

The sporadic simple group F2 known as Fischer's Baby Monster acts flag-transitively on a rank 5 P-geometry G(F2). P-geometries are geometries with string diagrams, all of whose nonempty edges except one are projective planes of order 2 and one terminal edge is the geometry of the Petersen graph. Let AC be a flag-transitive P-geometry of rank 5. Suppose that each proper residue of K is isomorphi...

Local Subgroups of the Monster and Odd Code Loops

The main result of this work is an explicit construction of p-local subgroups of the Monster, the largest sporadic simple group. The groups constructed are the normalizers in the Monster of certain subgroups of order 32 , 52 , and 72 and have shapes 32+5+10-(Af11 xGL(2, 3)), 52+2+4-(S3xGL(2, 5)), and 72+1+2 • GL(2, 7). These groups result from a general construction which proceeds in three step...

A New Construction of the Baby Monster and Its Applications

In this paper we show how to construct 4370 x 4370 matrices over GF(2), generating Fischer's {3,4}transposition group B, popularly known as the Baby Monster. This for the first time gives a construction which permits effective calculations to be performed in this very large simple group. We use this to give a new existence proof, and describe briefly applications to subgroup structure, geometry...

2A-orbifold construction and the baby-monster vertex operator superalgebra

In this article we prove that the full automorphism group of the baby-monster vertex operator superalgebra constructed by Höhn is isomorphic to 2×B, where B is the baby-monster sporadic finite simple group, and determine irreducible modules for the baby-monster vertex operator algebra. Our result has many corollaries. In particular, we can prove that the Z2-orbifold construction with respect to...