Given a transitive permutation group of degree n, we denote by e(T) (G) the expected number of elements of G which have to be drawn at random, with replacement, before a set of generators of a transitive subgroup of G is found. We compare e(T) (Sym(n)) and e(T) (Alt(n)).
Comparing the expected number of random elements from the symmetric and the alternating groups needed to generate a transitive subgroup
andrea lucchini;mariapia moscatiello
2019
Abstract
Given a transitive permutation group of degree n, we denote by e(T) (G) the expected number of elements of G which have to be drawn at random, with replacement, before a set of generators of a transitive subgroup of G is found. We compare e(T) (Sym(n)) and e(T) (Alt(n)).
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