In several papers the probability that t randomly chosen elements of a group G generate G itself has been studied. This study has been carried on finite groups and later extended to profinite groups. We discuss some possible applications of these ideas in other similar situations, analyzing the probability that t random elements generate a nilpotent subgroup, a solvable subgroup, a normal subgroup or a transitive subgroup.
Some generalizations of the probabilistic zeta function.
DETOMI, ELOISA MICHELA;LUCCHINI, ANDREA
2007
Abstract
In several papers the probability that t randomly chosen elements of a group G generate G itself has been studied. This study has been carried on finite groups and later extended to profinite groups. We discuss some possible applications of these ideas in other similar situations, analyzing the probability that t random elements generate a nilpotent subgroup, a solvable subgroup, a normal subgroup or a transitive subgroup.
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