Construction of a 45,694-dimensional simple module of Lyons' sporadic group over GF(2)

Gollan, Holger W.; Michler, Gerhard O.

doi:10.1016/s0024-3795(96)00002-x

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Cited by 2 publications

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“…If G = H N , we can choose χ to be the rational, irreducible complex character of 2-defect zero and degree 3 424 256. If G = L y, then it is proved in [7] that one can take a = 0 and χ to be the unique rational, irreducible complex character of degree 45 694.…”

Section: Simple Groupsmentioning

confidence: 99%

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Brauer characters with cyclotomic field of values

Navarro

Tiep

Turull

2008

Journal of Pure and Applied Algebra

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Section: Simple Groupsmentioning

confidence: 99%

“…Finally, assume t = 7 and G is of type E 6 or 2 E 6 . Then T contains F 4 (7) > Ω + 8 (7). By [14], Ω + 8 (7) > Ω + 8 (2), and we can choose s to be any element of order 5 in Ω + 8 (2).…”

Section: Simple Groupsmentioning

confidence: 99%

Brauer characters with cyclotomic field of values

Navarro

Tiep

Turull

2008

Journal of Pure and Applied Algebra

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Constructing Permutation Representations for Matrix Groups

Cooperman

Finkelstein

Tselman

et al. 1997

Journal of Symbolic Computation

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New techniques, both theoretical and practical, are presented for constructing permutation representations for computing with matrix groups defined over finite fields. The permutation representation is constructed on a conjugacy class of subgroups of prime order. We construct a base for the permutation representation, which in turn simplifies the computation of a strong generating set. In addition, we present an elementary test for checking the simplicity of the permutation image.The theory has been successfully tested on a representation of the sporadic simple group Ly, discovered by Lyons (1972). With no a priori assumptions, we find a permutation representation of degree 9 606 125 on a conjugacy class of subgroups of order 3, find the order of the resulting permutation group, and verify simplicity. A Monte Carlo variation of the algorithm was used to achieve better space and time efficiency. The construction of the permutation representation required four CPU days on a SPARCserver 670MP with 64 MB. The permutation representation was used implicitly in the sense that the group element was stored as a matrix, and its permutation action on a "point" was determined using a pre-computed data structure. Thus, additional computations required little additional space. The algorithm has also been implemented using the MasPar MP-1 SIMD parallel computer and 8 SPARC-2's running under MPI. The results of those parallel experiments are briefly reviewed.

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Construction of a 45,694-dimensional simple module of Lyons' sporadic group over GF(2)

Cited by 2 publications

References 5 publications

Brauer characters with cyclotomic field of values

Brauer characters with cyclotomic field of values

Constructing Permutation Representations for Matrix Groups

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