Asymptotic results for primitive permutation groups

[摘要] We prove that the number of conjugacy classes of primitive permutation groups of degree n is at most n(c mu(n)), where mu(n) denotes the maximal exponent occurring in the prime factorization of n. This result is applied to investigating maximal subgroup growth of infinite groups. We then proceed by showing that if the point-stabilizer G(alpha) of a primitive group G of degree n does not have the alternating group Alt(d) as a section, then the order of G is bounded by a polynomial in n. This result extends a well-known theorem of Babai, Cameron and Palfy. It is used to prove, for example, that if H is a subgroup of index n in a group G, and H is a product of b cyclic groups, then \G: H-G\ less than or equal to n(c) where c depends on b. (C) 1997 Academic Press.

[发布日期] 1997-02-01