Constructing permutation representations for large matrix groups

Cooperman, Gene; Finkelstein, Larry; York, Bryant W.; Tselman, Michael

doi:10.1145/190347.190384

Cited by 12 publications

(13 citation statements)

References 20 publications

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“…Using Algorithm 2.3.1 of [6] M. Weller [17] strengthened the results of Cooperman et al [5] as follows: Theorem 2.1. Let K be a finite field of characteristic p > 0.…”

Section: Transformation Of G Into a Permutation Groupmentioning

confidence: 86%

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A new Existence Proof of Janko’s Simple Group J 4

Cooperman¹,

Lempken²,

Michler³

et al. 1999

Computational Methods for Representations of Groups and Algebras

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“…Using Algorithm 2.3.1 of [6] M. Weller [17] strengthened the results of Cooperman et al [5] as follows: Theorem 2.1. Let K be a finite field of characteristic p > 0.…”

Section: Transformation Of G Into a Permutation Groupmentioning

confidence: 86%

“…In [5] Cooperman, Finkelstein, York and Tselman have described a method for the transformation of a linear representation of a finite group κ : X → GL n (K) over a finite field K into a permutation representation π : X → S m , where m denotes the index of a given subgroup U of X.…”

Section: Transformation Of G Into a Permutation Groupmentioning

confidence: 99%

A new Existence Proof of Janko’s Simple Group J 4

Cooperman¹,

Lempken²,

Michler³

et al. 1999

Computational Methods for Representations of Groups and Algebras

View full text Add to dashboard Cite

“…In 1994, Cooperman, Finkelstein, Tselman and York [15,16] constructed a permutation representation of Lyons's group of degree 9,606,125 from matrix generators, and also produced a strong generating set. Their representation was of permutation degree 9,606,125 for Lyons's group acting on a conjugacy class of subgroups of order three.…”

Section: Related Workmentioning

confidence: 99%

“…Weller [38,39] also produced a permutation representation of Janko's J4 group, using some of the hashing techniques of [15,16] and the double coset trick of [23,24]. That work was used in a revised existence proof for Janko's group [19].…”

Section: Related Workmentioning

confidence: 99%

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A parallel architecture for disk-based computing over the Baby Monster and other large finite simple groups

Robinson

Cooperman

2006

Proceedings of the 2006 International Symposium on Symbolic and Algebraic Computation

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We outline a distributed, disk-based technique for computing over very large matrix groups. This technique is used to compute a permutation representation for the Baby Monster, a sporadic simple group that acts on 13,571,955,000 points. Its group order is approximately 4 × 10 33 . This is a landmark because it is 100 times larger than any previous construction of a permutation representation. By using the computed on-disk data structures, computation over the Baby Monster is now feasible using the distributed disks of a cluster. Our work allows researchers to use either a matrix, a permutation, or a word representation for computing over the Baby Monster where previously only a matrix representation was available. The methodology is demonstrated by using as a signature the image of a vector that is stabilized by the maximal subgroup. The technique extends to finite simple groups and to other groups, through other signatures.

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On the Construction of the Finite Simple Groups with a Given Centralizer of a 2-Central Involution

Michler¹

2000

Journal of Algebra

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dedicated to helmut wielandt on the occasion of his 90th birthday Let H be a finite group having center Z H of even order. By the classical Brauer-Fowler theorem there can be only finitely many non-isomorphic simple groups G which contain a 2-central involution t for which C G t ∼ = H. In this article we give a deterministic algorithm constructing from the given group H all the finitely many simple groups G having an irreducible p-modular representation M over some finite field F of odd characteristic p > 0 with multiplicity-free semisimple restriction M H to H, if H satisfies certain natural conditions. As an application we obtain a uniform construction method for all the sporadic simple groups G not isomorphic to the smallest Mathieu group M 11 . Furthermore, it provides a permutation representation, and the character table of G.

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Constructing permutation representations for large matrix groups

Cited by 12 publications

References 20 publications

A new Existence Proof of Janko’s Simple Group J 4

A new Existence Proof of Janko’s Simple Group J 4

A parallel architecture for disk-based computing over the Baby Monster and other large finite simple groups

On the Construction of the Finite Simple Groups with a Given Centralizer of a 2-Central Involution

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