 About 13,500 results  books.google.com 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
References ... 

 books.google.com 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
... 

 books.google.com In fact the set of composition factors, and the multiplicity with which each appears,
depends only on M . A3 JordanHolder theorem Suppose that M is an Amodule
and that 0 = MI < • • • < Mt < Mk+i = M and 0 = NI < • • • < NI < N/+i = M are two ... 

 books.google.com 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
n ... 

 books.google.com 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 ... 

 books.google.com 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.
5. 

 books.google.com 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 ... 

 books.google.com 25 We will not classify all types of inequivalent symmetry groups of 3dimensional
lattices. ... X. Jordan's Theorem. For any n, a finite group G of motions of nspace
has an Abelian normal subgroup A whose index (G 1 A) in G is bounded by a ... 

 books.google.com 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 ndimensional representation and the alternating group AltnC1 is
... 

 books.google.com 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.) ... 

 