Abstract
We consider invariants of a finite group related to the number of random (independent, uniformly distributed) conjugacy classes that are required to generate it. These invariants are intuitively related to problems of Galois theory. We find group-theoretic expressions for them and investigate their values both theoretically and numerically.
Notes
1After the first version of this paper appeared as a preprint, some new results appeared in [CitationKantor et al. 10]; see the remarks at the end of Section 4.
2This means distributed in proportion to the size of the conjugacy class.
3Alternatively, following [CitationDixon 92], one says that elements (g 1, … , gm ) invariably generate G if their conjugacy classes generate G in the above sense.
4Note that this depends on the underlying group G.
5The trivial bound in trying to estimate c(G) in terms of |G| is easily seen to be c(G)⩽|G|2.
6This conjecture is imprecisely formulated in [CitationDixon 92], where the “expected number of elements needed to generate invariably” seems to mean any r(n) for which
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