• Corpus ID: 15230404

New computations in the Monster

@inproceedings{Linton2006NewCI,
  title={New computations in the Monster},
  author={Steve Linton and Eamonn A. O'Brien},
  year={2006}
}
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). 
5 Citations
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References

SHOWING 1-10 OF 28 REFERENCES
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
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
Computing in the Monster
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
A construction of the Monster simple group is described 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.
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