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- Title
Dixon's asymptotic without the classification of finite simple groups.
- Authors
Eberhard, Sean
- Abstract
Without using the classification of finite simple groups (CFSG), we show that the probability that two random elements of Sn$$ {S}_n $$ generate a primitive group smaller than An$$ {A}_n $$ is at most exp(−c(nlogn)1/2)$$ \exp \left(-c{\left(n\log n\right)}^{1/2}\right) $$. As a corollary we get Dixon's asymptotic expansion 1−1/n−1/n2−4/n3−23/n4−⋯$$ 1-1/n-1/{n}^2-4/{n}^3-23/{n}^4-\cdots $$for the probability that two random elements of Sn$$ {S}_n $$ (or An$$ {A}_n $$) generate a subgroup containing An$$ {A}_n $$.
- Subjects
FINITE simple groups; ASYMPTOTIC expansions; CLASSIFICATION; PERMUTATION groups
- Publication
Random Structures & Algorithms, 2024, Vol 64, Issue 4, p1016
- ISSN
1042-9832
- Publication type
Article
- DOI
10.1002/rsa.21205