منابع مشابه
On a Theorem of Jordan
The theorem of Jordan which I want to discuss here dates from 1872. It is an elementary result on finite groups of permutations. I shall first present its translations in Number Theory and Topology. 1. Statements 1.1. Number theory. Let f = ∑n m=0 amx m be a polynomial of degree n, with coefficients in Z. If p is prime, let Np(f) be the number of zeros of f in Fp = Z/pZ. Theorem 1. Assume (i) n...
متن کاملThe Jordan-Hölder Theorem
This submission contains theories that lead to a formalization of the proof of the Jordan-Hölder theorem about composition series of finite groups. The theories formalize the notions of isomorphism classes of groups, simple groups, normal series, composition series, maximal normal subgroups. Furthermore, they provide proofs of the second isomorphism theorem for groups, the characterization theo...
متن کاملThe Jordan-Hölder Theorem
The goal of this article is to formalize the Jordan-Hölder theorem in the context of group with operators as in the book [5]. Accordingly, the article introduces the structure of group with operators and reformulates some theorems on a group already present in the Mizar Mathematical Library. Next, the article formalizes the Zassenhaus butterfly lemma and the Schreier refinement theorem, and def...
متن کاملA Decomposition Theorem for Domains
A domain constructor that generalizes the product is de ned. It is shown that with this constructor exactly the prime-algebraic coherent Scott-domains and the empty set can be generated from two-chains and boolean at domains. 3 List of Symbols I am identifying the symbols by the corresponding Latex(+Amssymb)-symbols. " uparrow # downarrow ! rightarrow ? bot > top leq geq 2 in W bigvee V bigwedg...
متن کاملThe Jordan-Brouwer theorem for graphs
We prove a discrete Jordan-Brouwer-Schoenflies separation theorem telling that a (d − 1)-sphere H embedded in a d-sphere G defines two different connected graphs A,B in G such a way that A ∩B = H and A ∪B = G and such that the complementary graphs A,B are both d-balls. The graph theoretic definitions are due to Evako: the unit sphere of a vertex x of a graph G = (V,E) is the graph generated by ...
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: Colloquium Mathematicum
سال: 2004
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm101-1-1