Comparing the expected number of random elements from the symmetric and the alternating groups needed to generate a transitive subgroup

Andrea Lucchini, Mariapia Moscatiello

Abstract


Given a transitive permutation group of degree n, we denote by eT(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 eT(Sym(n)) and eT(Alt(n)).


Keywords


Transitive groups, generation, expectation

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DOI: https://doi.org/10.26493/1855-3974.1664.4b6

ISSN: 1855-3974

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