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2006•International Journal of Algebra and ComputationRequires access

PROBABILISTIC GENERATION OF WREATH PRODUCTS OF NON-ABELIAN FINITE SIMPLE GROUPS, II

Martyn Quick

Open publisher page 15 citations

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.

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What this paper is about

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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OpenAlex reports 15 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available 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.

Key concepts: Wreath product, Mathematics, Profinite group, Abelian group, Iterated function, Simple (philosophy), Classification of finite simple groups, Simple group

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