Almost all alternating groups are invariably generated by two elements of prime order

Abstract

We show that for all $n\le X$ 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.

11 pages; Referee comments incorporated; to appear in IMRN

References in corpus (3)

• Almost primes in almost all short intervals II
• On invariable generation of alternating groups by elements of prime and prime power order
• On the probability of generating invariably a finite simple group

Cited by in corpus (2)

• On invariable generation of alternating groups by elements of prime and prime power order
• Invariable generation of finite simple groups and rational homology of coset posets