About 13,500 results
|This is called the FUNDAMENTAL THEOREM OF SYMMETRIC FUNCTIONS. ... |
́N THEOREM, FINITE GROUP, JORDAN'S SYMMETRIC GROUP THEOREM,
NETTO'S CONJECTURE, PARTITION FUNCTION P, SIMPLE GROUP
|If G is primitive and contains a transposition, a theorem of C. Jordan asserts that |
G is the full symmetric group on Q, and so, of course, it is multiply transitive. We
will obtain this result as a corollary of a much more general theorem, also due to
|In fact the set of composition factors, and the multiplicity with which each appears, |
depends only on M . A3 Jordan-Holder theorem Suppose that M is an A-module
and that 0 = MI < • • • < Mt < Mk+i = M and 0 = NI < • • • < NI < N/+i = M are two ...
|6.1 Finitary permutation groups A permutation of an infinite set ft is finitary if it |
moves only finitely many points. ... from a theorem of Jordan, according to which
there is a function / such that, if G is a finite primitive permutation group of degree
|Some celebrated theorems of the time were about permutation groups, and were |
essentially so in the sense that their ... group of degree n but is not alternating or
symmetric then / < «/3 (a theorem proved by Mathieu in 1861, which Jordan ...
|Hence G contains An and is either An or Sn. On the other hand, if P contains a |
single cycle of p letters, then Theorem 5.6.2 ... as that of Jordan's theorem, the
only other group satisfying the hypotheses being the 72 Permutation Groups [Ch.
|An application of Theorem 13.1 is the important theorem: Theorem 13.2. If G is |
primitive on Q and G4 is primitive on 9 – A = T, and in addition, 1 < | T = m = n = |
Q |, then G is (n – m + 1)-fold primitive (Jordan, 1871). We prove this theorem by ...
|25 We will not classify all types of inequivalent symmetry groups of 3-dimensional |
lattices. ... X. Jordan's Theorem. For any n, a finite group G of motions of n-space
has an Abelian normal subgroup A whose index (G 1 A) in G is bounded by a ...
|A group G is called a Jordan group if there exists a positive integer d, depending |
on G only, such that every finite ... Jordan's Theorem The first example that led to
Definition 1 justifies the coined name. ... Since the symmetric group SymnC1
admits a faithful n-dimensional representation and the alternating group AltnC1 is
|He then “completed” the proof of the Jordan– Hölder theorem, namely that the |
quotient groups in a composition series are ... (Previously they were considered
in concrete cases—as permutation groups, transformation groups, and so on.) ...