Affiliation:
1. Department of Mathematics and Statistics , University of Turku, 20014 Turku, Finland
Abstract
Abstract
We show that for all $n\leq X$ apart from $O(X\exp (-c(\log X)^{1/2}(\log \log X)^{1/2}))$ exceptions, the alternating group $A_{n}$ is invariably generated by two elements of prime order. This answers (in a quantitative form) a question of Guralnick, Shareshian, and Woodroofe.
Publisher
Oxford University Press (OUP)
Reference18 articles.
1. Simple groups admit Beauville structures;Guralnick;J. Lond. Math. Soc. (2),2012
2. Invariable generation and the Chebotarev invariant of a finite group;Kantor;J. Algebra.,2011
3. The probability of generating the symmetric group;Dixon;Math. Z.,1969
4. Invariable generation of the symmetric group;Eberhard;Duke Math. J.,2017
5. On the probability of generating invariably a finite simple group;Garzoni,2020
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