Conway's group and octonions

  title={Conway's group and octonions},
  author={Robert A. Wilson},
  journal={Journal of Group Theory},
  pages={1 - 8}
Abstract We give a description of the double cover of Conway's group in terms of right multiplications by 3 × 3 matrices over the octonions. This leads to simple sets of generators for many of the maximal subgroups, including a uniform construction of the Suzuki chain of subgroups. 
As a contribution to an eventual solution of the problem of the determination of the maximal subgroups of the Monster we show that there is no subgroup isomorphic to Sz(8). This also completes theExpand
U-Duality and the Leech Lattice
It has recently been shown that the full automorphism group of the Leech lattice, Conway's group Co_0, can be generated by 3 x 3 matrices over the octonions. We show such matrices are of type F_4 inExpand
On infinitely generated groups whose proper subgroups are solvable
Abstract In this work infinitely generated groups are considered whose proper subgroups are solvable and in whose homomorphic images finitely generated subgroups have residually nilpotent normalExpand


Octonions and the Leech lattice
Abstract We give a new, elementary, description of the Leech lattice in terms of octonions, thereby providing the first real explanation of the fact that the number of minimal vectors, 196560, can beExpand
On Quaternions and Octonions
This book investigates the geometry of quaternion and octonion algebras. Following a comprehensive historical introduction, the book illuminates the special properties of 3- and 4-dimensionalExpand
On quaternions and octonions: Their geometry, arithmetic, and symmetry, by John H. Conway and Derek A. Smith. Pp. 159. $29. 2003. ISBN 1 5688 134 9 (A. K. Peters).
various different methods and approaches, and the power in the appropriate use of language and notation in mathematics. Much of the text and most the examples are presented in a concrete manner, butExpand
Finite Quaternionic Reflection Groups
In this article the quaternionic reflection groups are classified. Such a group is defined so as to generalize the notion of reflection groups appearing in [4, 171, i.e., it is a group of linearExpand
Bull. London Math. Soc
  • Bull. London Math. Soc
  • 1969