The Transitivity, Primitivity and Faithfulness of Wreath Products of Permutation groups
نویسندگان
چکیده
منابع مشابه
Wreath Products of Permutation Classes
A permutation class which is closed under pattern involvement may be described in terms of its basis. The wreath product construction X o Y of two permutation classes X and Y is also closed, and we investigate classes Y with the property that, for any finitely based class X, the wreath product X o Y is also finitely based.
متن کاملWreath Decompositions of Finite Permutation Groups
There is a familiar construction with two finite, transitive permutation groups as input and a finite, transitive permutation group, called their wreath product, as output. The corresponding 'imprimitive wreath decomposition concept is the first subject of this paper. A formal definition is adopted and an overview obtained for all such decompositions of any given finite, transitive group. The r...
متن کاملPrimitivity of Permutation Groups, Coherent Algebras and Matrices
A coherent algebra is F-primitive if each of its non-identity basis matrices is primitive in the sense of Frobenius. We investigate the relationship between the primitivity of a permutation group, the primitivity of its centralizer algebra, and F-primitivity. The results obtained are applied to give new proofs of primitivity criteria for the exponentiations of permutation groups and of coherent...
متن کاملThree Types of Inclusions of Innately Transitive Permutation Groups into Wreath Products in Product Action
A permutation group is innately transitive if it has a transitive minimal normal subgroup, and this subgroup is called a plinth. In this paper we study three special types of inclusions of innately transitive permutation groups in wreath products in product action. This is achieved by studying the natural Cartesian decomposition of the underlying set that correspond to the product action of a w...
متن کاملWreath Products and Existentially Complete Solvable Groups
It is known that the theory of abelian groups has a model companion but that the theory of groups does not. We show that for any fixed 22 a 2 the theory of groups solvable of length s 22 has no model companion. For the metabelian case (22 = 2) we prove the stronger result that the classes of finitely generic, infinitely generic, and existentially complete metabelian groups are all distinct. We ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: IOSR Journal of Mathematics
سال: 2014
ISSN: 2319-765X,2278-5728
DOI: 10.9790/5728-10350104