Probabilistic generation of wreath products of non-abelian finite simple groups, II

Martyn Quick

doi:10.1142/S0218196706003074

Probabilistic generation of wreath products of non-abelian finite simple groups, II

Martyn Quick

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

We show that the probability of generating an iterated wreath product of non-abelian finite simple groups converges to 1 as the order of the first simple group tends to infinity provided the wreath products are constructed with transitive and faithful actions. This has the consequence that the profinite group which is the inverse limit of these iterated wreath products is positively finitely generated.

Original language	English
Pages (from-to)	493-503
Number of pages	11
Journal	International Journal of Algebra and Computation
Volume	16
Issue number	3
DOIs	https://doi.org/10.1142/S0218196706003074
Publication status	Published - Jun 2006

Keywords

groups
generation
wreath product
probability

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10.1142/S0218196706003074

Cite this

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title = "Probabilistic generation of wreath products of non-abelian finite simple groups, II",

abstract = "We show that the probability of generating an iterated wreath product of non-abelian finite simple groups converges to 1 as the order of the first simple group tends to infinity provided the wreath products are constructed with transitive and faithful actions. This has the consequence that the profinite group which is the inverse limit of these iterated wreath products is positively finitely generated.",

keywords = "groups, generation, wreath product, probability",

author = "Martyn Quick",

note = "Completion of work begun in M. Quick, {"}Probabilistic generation of wreath products of non-abelian finite simple groups,{"} Comm. Algebra 32 (2004), 4753-4768.",

year = "2006",

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PY - 2006/6

Y1 - 2006/6

N2 - We show that the probability of generating an iterated wreath product of non-abelian finite simple groups converges to 1 as the order of the first simple group tends to infinity provided the wreath products are constructed with transitive and faithful actions. This has the consequence that the profinite group which is the inverse limit of these iterated wreath products is positively finitely generated.

AB - We show that the probability of generating an iterated wreath product of non-abelian finite simple groups converges to 1 as the order of the first simple group tends to infinity provided the wreath products are constructed with transitive and faithful actions. This has the consequence that the profinite group which is the inverse limit of these iterated wreath products is positively finitely generated.

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KW - generation

KW - wreath product

KW - probability

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JO - International Journal of Algebra and Computation

JF - International Journal of Algebra and Computation

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ER -

Probabilistic generation of wreath products of non-abelian finite simple groups, II

Abstract

Keywords

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EP/C523229/1: Multidisciplinary Critical Mass in Computational Algebra and Applications

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Probabilistic generation of wreath products of non-abelian finite simple groups, II

Abstract

Keywords

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EP/C523229/1: Multidisciplinary Critical Mass in Computational Algebra and Applications

Cite this