In mathematics, a permutation group G acting on a non-empty finite set X is called primitive if G acts transitively on X and the only partitions the G-action...

mathematics, a permutation group is a group G whose elements are permutations of a given set M and whose group operation is the composition of permutations in G...

E.; Saxl, J. (1988), "On the O'Nan–Scott theorem for finite primitive permutation groups", Journal of the Australian Mathematical Society, 44 (3): 389–396...

Oligomorphic group O'Nan–Scott theorem Parker vector Permutation group Place-permutation action Primitive permutation group Rank 3 permutation group Representation...

function or antiderivative, F′ = f Primitive permutation group Primitive root of unity; See Root of unity Primitive triangle, an integer triangle whose sides...

the idea was first noticed, is that of finite groups (see primitive permutation group). Consider a group G and subgroups H and K, with K contained in H...

In finite group theory, Jordan's theorem states that if a primitive permutation group G is a subgroup of the symmetric group Sn and contains a p-cycle...

one of the most influential theorems of permutation group theory; the classification of finite simple groups is what makes it so useful. Originally the...

a result in group theory, originally proposed by Charles Sims. He conjectured that if G {\displaystyle G} is a primitive permutation group on a finite...

conjugate to Gx because Ggx = g ⋅ Gx ⋅ g−1). Seress, Ákos (2003), Permutation Group Algorithms, Cambridge Tracts in Mathematics, vol. 152, Cambridge University...

Several of the sporadic simple groups were discovered as rank 3 permutation groups. The primitive rank 3 permutation groups are all in one of the following...

theory of permutation groups such as the order of an element of a group, conjugacy, and the cycle decomposition of elements of permutation groups. Ruffini...

them. For a more elementary discussion of Galois groups in terms of permutation groups, see the article on Galois theory. Suppose that E {\displaystyle E}...

Although the group of all permutations of a set depends formally on the set, the concept of group action allows one to consider a single group for studying...

implementation worked on a 256 node grid and so included the following permutation table: int permutation[] = { 151, 160, 137, 91, 90, 15, 131, 13, 201, 95, 96, 53...

numbers between 5 and 31, inclusively, is 155. There are 143 primitive permutation groups of degree 81. OEIS: A000019 If one adds up all the primes from...

All but one of the sporadic transitive linear groups G {\displaystyle G} yield a primitive permutation group p d : G {\displaystyle p^{d}:G} of degree at...

number of values. If g is a primitive root modulo n and n is prime, then the period of repetition is n − 1. Permutations created in this way (and their...

2. Such multiply transitive permutation groups can be defined for any natural number k. Specifically, a permutation group G acting on n points is k-transitive...

simple groups. With Jan Saxl and Martin Liebeck, she has co-authored papers on many topics including: permutation groups, primitive permutation groups, simple...

specific cases of geometric transformation groups, symmetry groups, permutation groups, and automorphism groups, the symbol ∘ {\displaystyle \circ } is often...

equations that are solvable by radicals in terms of properties of the permutation group of their roots—an equation is by definition solvable by radicals if...

groups in two dimensions. Other finite subgroups include: Permutation matrices (the Coxeter group An) Signed permutation matrices (the Coxeter group Bn);...

examples of finite groups include cyclic groups and permutation groups. The study of finite groups has been an integral part of group theory since it arose...

copies of another group, somewhat analogous to exponentiation. Wreath products are used in the classification of permutation groups and also provide a...

symmetric group of permutations, the dihedral groups, and more generally all finite real reflection groups (the Coxeter groups or Weyl groups, including...

follows that A ( α ) {\displaystyle A(\alpha )} is the permutation matrix corresponding to the permutation of G which sends each σ i {\displaystyle \sigma _{i}}...

A one-way permutation is a one-way function that is also a permutation—that is, a one-way function that is bijective. One-way permutations are an important...

(typically characters or groups of characters) according to a regular system to produce a ciphertext which is a permutation of the plaintext. They differ...

Martin; Praeger, Cheryl; Saxl, Jan (2010). "Regular subgroups of primitive permutation groups". Memoirs of the American Mathematical Society. 203 (952). American...