We give explicit, asymptotically sharp bounds for the probability that a pair of random permutations of degree n generates either Symm(n) or Alt(n) and also for the probability that a pair of even random permutations of degree n generate Alt(n). As an application we answer a question of Wiegold in the case of alternating groups.
Maroti, A., Tamburini Bellani, M. C., Bounds for the probability of generating the symmetric and alternating groups, <<ARCHIV DER MATHEMATIK>>, 2011; Vol. 96 (2): 115-121 [http://hdl.handle.net/10807/1624]
Bounds for the probability of generating the symmetric and alternating groups
Maroti, Attila;Tamburini Bellani, Maria Clara
2011
Abstract
We give explicit, asymptotically sharp bounds for the probability that a pair of random permutations of degree n generates either Symm(n) or Alt(n) and also for the probability that a pair of even random permutations of degree n generate Alt(n). As an application we answer a question of Wiegold in the case of alternating groups.
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