Orbits of soluble in nite permutation groups
نویسنده
چکیده
منابع مشابه
The Schreier-Sims algorithm
A base and strong generating set provides an effective computer representation for a permutation group. This representation helps us to calculate the group order, list the group elements, generate random elements, test for group membership and store group elements efficiently. Knowledge of a base and strong generating set essentially reduces these tasks to the calculation of certain orbits. Giv...
متن کاملSome counting problems related topermutation
This paper discusses investigations of sequences of natural numbers which count the orbits of an innnite permutation group on n-sets or n-tuples. It surveys known results on the growth rates, cycle index techniques, and an interpretation as the Hilbert series of a graded algebra, with a possible application to the question of smoothness of growth. I suggest that these orbit-counting sequences a...
متن کاملComputing automorphisms of finite soluble groups
There is a large collection of e ective algorithms for computing information about nite soluble groups. The success in computation with these groups is primarily due to a computationally convenient representation of them by means of (special forms of) power conjugate presentations. A notable omission from this collection of algorithms is an e ective algorithm for computing the automorphism grou...
متن کاملInfinite Permutation Groups in Enumeration and Model Theory
A permutation group G on a set Q has a natural action on Q for each natural number n. The group is called oligomorphic if it has only finitely many orbits on Q for all «GN. (The term means "few shapes". Typically our permutation groups are groups of automorphisms of structures of some kind; oligomorphy implies that the structure has only finitely many non-isomorphic w-element substructures for ...
متن کاملSequences realized as Parker vectors of oligomorphic permutation groups
The purpose of this paper is to study the Parker vectors (in fact, sequences) of several known classes of oligomorphic groups. The Parker sequence of a group G is the sequence that counts the number of G-orbits on cycles appearing in elements of G. This work was inspired by Cameron’s paper on the sequences realized by counting orbits on k-sets and k-tuples.
متن کامل