منابع مشابه
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...
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Given a set S with n elements, consider all the possible one-to-one and onto functions from S to itself. This collection of functions is called the permutation group of S, because the functions are simply permuting the elements of S. We notice immediately that it doesn’t matter what the elements of S are (numbers, planets, tacos, etc) just that there are n distinct ones in the set, so we may re...
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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: Involve, a Journal of Mathematics
سال: 2014
ISSN: 1944-4184,1944-4176
DOI: 10.2140/involve.2014.7.41