• Corpus ID: 15230404

New computations in the Monster

  title={New computations in the Monster},
  author={Steve Linton and Eamonn A. O'Brien},
We survey recent computational results concerning the Monster sporadic simple group. The main results are: progress towards a complete classification of the maximal subgroups, including showing that L2(27) is not a subgroup; showing that the 196882-dimensional module over GF (2) supports a quadratic form; a complete set of explicit conjugacy class representatives; small representations of most of the maximal subgroups; and a partial classification of the ‘nets’ (in the sense of Norton). 
4 Citations
Solvable Subgroups of Maximal Order in Sporadic Simple Groups
We determine the orders of solvable subgroups of maximal orders in sporadic simple groups and their automorphism groups, using the information in the Atlas of Finite Groups [CCN + 85] and the GAP
GAP Computations Concerning Hamiltonian Cycles in the Generating Graphs of Finite Groups
This is a collection of examples showing how the GAP system can be used to compute information about the generating graphs of finite groups. It includes all examples that were needed for the
Group Theory Permutation Groups
Finite Groups 20Dxx [1] A. Adem, J. F. Carlson, D. B. Karagueuzian, and R. James Milgram, The cohomology of the Sylow 2-subgroup of the Higman-Sims group, J. Pure Appl. Algebra 164 (2001), no. 3,
Impartial avoidance games for generating finite groups
We study an impartial avoidance game introduced by Anderson and Harary. The game is played by two players who alternately select previously unselected elements of a finite group. The first player who


Anatomy of the Monster: II
We describe the current state of progress on the maximal subgroup problem for the Monster sporadic simple group. Any unknown maximal subgroup is an almost simple group whose socle is in one of 19
A New Maximal Subgroup of the Monster
We use our computer construction of the Monster sporadic simple group M to find a new maximal subgroup PGL2(29). In particular, we prove containment of L2(29) in M, thereby answering a long-standing
Conjugacy Class Representatives in the Monster Group
The paper describes a procedure for determining (up to algebraic conjugacy) the conjugacy class in which any element of the Monster lies, using computer constructions of representations of the
Computing in the Monster
  • S. Norton
  • Computer Science, Mathematics
    J. Symb. Comput.
  • 2001
We discuss the feasibility of a general technique for computing in the Fischer?Griess Monster, and provide information on some of its subgroups which illustrates the use of computational techniques
The Monster is a Hurwitz group
We describe explicit calculations to nd generators a and b for the Monster sporadic simple group, satisfying the relations a 2 = b 3 = (ab) 7 = 1.
A New Computer Construction of the Monster Using 2-Local Subgroups
We describe a construction of the Monster simple group implicitly as 196882 × 196882 matrices over the field of 3 elements.
Maximal 2-local subgroups of the Monster and Baby Monster
The lists of the maximal 2-local subgroups of the Monster and Baby Monster simple groups in the Atlas are complete.