Zassenhaus' theorem supersedes the Jordan-Hölder theorem
نویسندگان
چکیده
منابع مشابه
The 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...
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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...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1979
ISSN: 0001-8708
DOI: 10.1016/0001-8708(79)90022-7