A New Existence Proof for Ly, the Sporadic Simple Group of R. Lyons

Gollan, Holger W.

doi:10.1006/jsco.2000.1010

Cited by 8 publications

(17 citation statements)

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“…[5] to give a new existence proof of Janko's large sporadic group J 4 . In [8] Gollan constructed Lyons simple group Ly in a similar way. In [14] Kratzer gave an existence proof for the Rudvalis group Ru by means of Algorithm 4.6.…”

Section: A Uniform Construction Methods For 25 Sporadic Groupsmentioning

confidence: 97%

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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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Section: A Uniform Construction Methods For 25 Sporadic Groupsmentioning

confidence: 97%

“…In order to compute the precise order of the group G of Theorem 4.1, one has to be able to decide whether the subgroup U of G equals the stabilizer U. This is done by the following algorithm due to C. Sims (unpublished) and Gollan [8]. Double coset trick).…”

Section: From Matrix Groups To Permutation Groups and Character Tablesmentioning

confidence: 99%

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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“…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%

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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“…For this sort of application, Sims' relations are rather cumbersome. In [5,6] Gollan also gives a new presentation for the Lyons group and this presentation is improved in [4]. These new presentations have similar drawbacks to that of Sims.…”

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confidence: 99%

“…, Z. Thus, for example, when we write M 2 ∼ 3 6 .2 3 .Sym (5), we are stating only that M 2 has a normal subgroup of order 3 6 , a normal subgroup of order 3 6 · 2 3 , both with unspecified structure, and a quotient isomorphic to Sym (5). As in the ATLAS [3], we denote a non-split extension of a group A by a group B by A .…”

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confidence: 99%