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The Covering Radius of the Leech Lattice
We investigate the points in 24-dimensional space that are at maximal distance from the Leech lattice, i.e. the “deep holes” in that lattice.
Computer construction of the Monster
This paper describes the computer construction of the largest of the 26 sporadic simple groups, the so-called Monster, which is described in detail in this paper.
The Maximal Subgroups of the Fischer Group Fi23
A method for building permutation representations of finitely presented groups
We design an algorithm to find certain partial permutation representations of a finitely presented group $G$ (the bricks) that may be combined to a transitive permutation representation of $G$ (the…
The minimal 5-representation of Lyons' sporadic group
The Lyons simple group was first constructed by Sims  as a permutation group on 8835156 points. This representation is, because of its size, not very useful for calculating in the group. In this…
Computational Modular Character Theory
This book describes some computational methods to deal with modular characters of finite groups. It is the theoretical background of the MOC system of the same authors. This system was, and is still…
Polynomial-time proofs that groups are hyperbolic
The Computer Construction of Matrix Representations of Finite Groups over Finite Fields
On extremal even unimodular 72-dimensional lattices
By computer search we show that the lattice Γ from  is the unique extremal even unimodular 72-dimensional lattices that can be constructed as proposed in .
The 5-modular characters of the McLaughlin group and its covering group
In the present paper we determine the 5-modular decomposition matrices for the sporadic group 3.G - 3McL, the triple cover of the McLaughlin group. There are only blocks of defect 0 and blocks of…