Group Membership for Groups with Primitive Orbits
نویسنده
چکیده
This paper considers a permutation group G = 〈S〉 of degree n with t orbits such that the action on each orbit is primitive. It presents a O(tn2 logc(n)) time Monte Carlo group membership algorithm for some constant c. The algorithm is notable for its use of a new theorem showing how to find O(t log n) generators in O (̃|S|n) time under a more general form of the above hypotheses. The algorithm relies on new combinatorial methods for computing with groups [CF92] and previous work of Babai, Luks and Seress [BLS88]. In addition, it makes extensive use of a structure theorem for primitive groups by Cameron [Cam81], which can be derived from results of Kantor [Kan79] and the classification of finite simple groups.
منابع مشابه
The Topology on the Primitive Ideal Space of Transformation Group C # - Algebras and C.C.R. Transformation Group C # -Algebras
If (G, 8) is a second countable transformation group and the stability groups are amenable then C*(G, 8) is C.C.R. if and only if the orbits are closed and the stability groups are C.C.R. In addition, partial results relating closed orbits to C.C.R. algebras are obtained in the nonseparable case. In several cases, the topology of the primitive ideal space is calculated explicitly. In particular...
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