finite group theory, a rank 3 permutation group acts transitively on a set such that the stabilizer of a point has 3 orbits. The study of these groups was...

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...

Rudvalis group acts as a rank 3 permutation group on 4060 points, with one point stabilizer being the Ree group 2F4(2), the automorphism group of the Tits...

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

Schur multiplier: Order 2. Outer automorphism group: Order 2. Remarks: It acts as a rank 3 permutation group on the Higman Sims graph with 100 points, and...

19 · 31 ≈ 5×1011. The Rudvalis group is a finite simple group R {\displaystyle R} that is a rank 3 permutation group on 4060 letters where the stabilizer...

(the other is the Janko group J3). It was constructed by Marshall Hall and David Wales (1968) as a rank 3 permutation group on 100 points. Both the Schur...

abelian group – Commutative group where every element is the sum of elements from one finite subset Classification of Rank 3 permutation group – Five sporadic...

4×1011. Suz is one of the 26 Sporadic groups and was discovered by Suzuki (1969) as a rank 3 permutation group on 1782 points with point stabilizer G2(4)...

Zassenhaus group, named after Hans Zassenhaus, is a certain sort of doubly transitive permutation group very closely related to rank-1 groups of Lie type...

A permutation test (also called re-randomization test or shuffle test) is an exact statistical hypothesis test. A permutation test involves two or more...

the permutations of X (i.e. the bijective functions from X to X) fall into two classes of equal size: the even permutations and the odd permutations. If...

order. The classification of 2-transitive permutation groups. The classification of rank 3 permutation groups. The Sims conjecture Frobenius's conjecture...

cyclic group C2. Sims (1973) proved the existence of such a group and its uniqueness up to isomorphism with a combination of permutation group theory...

for other rank 3 permutation groups on 100 points. They soon focused on a possible one containing the Mathieu group M22, which has permutation representations...

In statistics, Spearman's rank correlation coefficient or Spearman's ρ is a number ranging from -1 to 1 that indicates how strongly two sets of ranks are...

one of the 26 sporadic groups and was discovered by Jack McLaughlin (1969) as an index 2 subgroup of a rank 3 permutation group acting on the McLaughlin...

Signed permutation matrices (the Coxeter group Bn); also equals the intersection of the orthogonal group with the integer matrices. The orthogonal group is...

way to encode each possible permutation of a sequence of n numbers. It is an instance of a scheme for numbering permutations and is an example of an inversion...

group Fi22. The group 2F4(2) also occurs as a maximal subgroup of the Rudvalis group, as the point stabilizer of the rank-3 permutation action on 4060 = 1 + 1755 + 2304...

the group axioms (e.g. st = suu−1t but s ≠ t−1 for s,t,u ∈ S). The members of S are called generators of FS, and the number of generators is the rank of...

establish properties of the group G. Permutation groups and matrix groups are special cases of transformation groups: groups that act on a certain space...

1873). They are multiply transitive permutation groups on 11, 12, 22, 23 or 24 objects. They are the first sporadic groups to be discovered. Sometimes the...

is a permutation sampled uniformly at random from S n {\textstyle S_{n}} , the permutation group on 1 : n {\textstyle 1:n} . For each permutation, its...

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

permutation representation is a rank 5 action on 2058 points with point stabilizer Sp4(4):2. The graph associated with this representation has rank 5...

Mathematical Society (LMS) Pólya Prize in 2020 O'Nan–Scott theorem Rank 3 permutation group Personal Profile of Prof. Martin Liebeck at Mathematical Sciences...

gives a rank 3 action on 55 points. M11 has a 3-transitive permutation representation on 12 points with point stabilizer PSL2(11). The permutation representations...

good. Alternatively, the null distribution can be approximated using permutation tests and Monte Carlo simulations. Some books tabulate statistics equivalent...

M24 is one of the 26 sporadic groups and was introduced by Mathieu (1861, 1873). It is a 5-transitive permutation group on 24 objects. The Schur multiplier...