Cycle-Closed Permutation Groups
نویسنده
چکیده
A finite permutation group is cycle-closed if it contains all the cycles of all of its elements. It is shown by elementary means that the cycle-closed groups are precisely the direct products of symmetric groups and cyclic groups of prime order. Moreover, from any group, a cycle-closed group is reached in at most three steps, a step consisting of adding all cycles of all group elements. For infinite groups, there are several possible generalisations. Some analogues of the finite result are proved.
منابع مشابه
On the tenacity of cycle permutation graph
A special class of cubic graphs are the cycle permutation graphs. A cycle permutation graph Pn(α) is defined by taking two vertex-disjoint cycles on n vertices and adding a matching between the vertices of the two cycles.In this paper we determine a good upper bound for tenacity of cycle permutation graphs.
متن کاملDigraph Representations of 2-closed Permutation Groups with a Normal Regular Cyclic Subgroup
In this paper, we classify 2-closed (in Wielandt’s sense) permutation groups which contain a normal regular cyclic subgroup and prove that for each such group G, there exists a circulant Γ such that Aut(Γ) = G.
متن کاملOrbit equivalence and permutation groups defined by unordered relations
For a set Ω an unordered relation on Ω is a family R of subsets of Ω . If R is such a relation we let G(R) be the group of all permutations on Ω that preserve R, that is g belongs to G(R) if and only if x ∈R implies x ∈R. We are interested in permutation groups which can be represented as G= G(R) for a suitable unordered relation R on Ω . When this is the case, we say that G is defined by the r...
متن کاملEconomic Lot Sizing and Scheduling in Distributed Permutation Flow Shops
This paper addresses a new mixed integer nonlinear and linear mathematical programming economic lot sizing and scheduling problem in distributed permutation flow shop problem with number of identical factories and machines. Different products must be distributed between the factories and then assignment of products to factories and sequencing of the products assigned to each factory has to be d...
متن کاملPolynomial aspects of codes, matroids and permutation groups
Index 74 Preface The three subjects of the title (codes, matroids, and permutation groups) have many interconnections. In particular, in each case, there is a polynomial which captures a lot of information about the structure: we have the weight enumerator of a code, the Tutte polynomial (or rank polynomial) of a matroid, and the cycle index of a permutation group. With any code is associated a...
متن کامل