Permutation Groups in Automata Diagrams

Cell Flipping in Permutation Diagrams

QUASI-PERMUTATION REPRESENTATIONS OF METACYCLIC 2-GROUPS

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...

Permutation 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,...

Permutation Groups in

We show that the basic problems of permutation group manipulation admit eecient parallel solutions. Given a permutation group G by a list of generators, we nd a set of NC-eecient strong generators in NC. Using this, we show, that the following problems are in NC: membership in G; determining the order of G; nding the center of G; nding a composition series of G along with permutation representa...

Galois 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 ...