A Reduction Algorithm for Large-Base Primitive Permutation Groups
نویسندگان
چکیده
منابع مشابه
The Minimal Base Size of Primitive Solvable Permutation Groups
A base of a permutation group G is a sequence B of points from the permutation domain such that only the identity of G fixes B pointwise. Answering a question of Pyber, we prove that all primitive solvable permutation groups have a base of size at most four.
متن کاملDistinguishing Primitive Permutation Groups
Let G be a permutation group acting on a set V . A partition π of V is distinguishing if the only element of G that fixes each cell of π is the identity. The distinguishing number of G is the minimum number of cells in a distinguishing partition. We prove that if G is a primitive permutation group and |V | ≥ 336, its distinguishing number is two.
متن کاملBases for Primitive Permutation Groups and a Conjecture of Babai
A base of a permutation group G is a sequence B of points from the permutation domain such that only the identity of G fixes B pointwise. We show that primitive permutation groups with no alternating composition factors of degree greater than d and no classical composition factors of rank greater than d have a base of size bounded above by a function of d. This confirms a conjecture of Babai. Q...
متن کاملSuborbits in Infinite Primitive Permutation Groups
For every infinite cardinal κ, we construct a primitive permutation group which has a finite suborbit paired with a suborbit of size κ. This answers a question of Peter M. Neumann.
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ژورنال
عنوان ژورنال: LMS Journal of Computation and Mathematics
سال: 2006
ISSN: 1461-1570
DOI: 10.1112/s1461157000001236