منابع مشابه
Cycle-Closed Permutation Groups
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 inf...
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By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. Thus, every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a fa...
متن کاملPermutation Groups
The theory of permutation groups is essentially the theory of symmetry for mathematical and physical systems. It therefore has major impact in diverse areas of mathematics. Twentieth-century permutation group theory focused on the theory of finite primitive permutation groups, and this theory continues to become deeper and more powerful as applications of the finite simple group classification,...
متن کاملOn 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 کاملGalois Groups as Permutation Groups
Writing f(T ) = (T − r1) · · · (T − rn), the splitting field of f(T ) over K is K(r1, . . . , rn). Each σ in the Galois group of f(T ) over K permutes the ri’s since σ fixes K and therefore f(r) = 0⇒ f(σ(r)) = 0. The automorphism σ is completely determined by its permutation of the ri’s since the ri’s generate the splitting field over K. A permutation of the ri’s can be viewed as a permutation ...
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 1996
ISSN: 0925-9899,1572-9192
DOI: 10.1007/bf00193181