# 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

Solvable Subgroups of Maximal Order in Sporadic Simple Groups

- Mathematics
- 2012

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…

Large maximal subgroups of finite almost simple groups

- Mathematics
- 2022

We prove in this paper that a ﬁnite almost simple group R with socle the non-abelian simple group S possesses a conjugacy class of maximal subgroups whose index coincides with the smallest index l( S…

Group Theory Permutation Groups

- Mathematics
- 2017

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

- Mathematics
- 2016

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…

Hamiltonian cycles in the generating graphs of finite groups

- Mathematics
- 2009

For a finite group G let Γ(G) denote the graph defined on the non‐identity elements of G in such a way that two distinct vertices are connected by an edge if and only if they generate G. In this…

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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…

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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…

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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…

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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.

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A construction of the Monster simple group is described implicitly as 196882×196882 matrices over the field of 3 elements.

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The lists of the maximal 2-local subgroups of the Monster and Baby Monster simple groups in the Atlas are complete.