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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...

In mathematics, a permutation of a set can mean one of two different things: an arrangement of its members in a sequence or linear order, or the act or...

Subgroups of symmetric groups are called permutation groups and are widely studied because of their importance in understanding group actions, homogeneous...

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...

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

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...

with permutation groups in such a setting, so in these applications, when a group is considered, it is a permutation representation of the group which...

in particular in group theory, a cyclic permutation is a permutation consisting of a single cycle. In some cases, cyclic permutations are referred to as...

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...

mathematical permutations. Alternating permutation Circular shift Cyclic permutation Derangement Even and odd permutations—see Parity of a permutation Josephus...

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}...

{\displaystyle G} as a group of permutations, or as a group of permutation matrices. The term also refers to the combination of the two. A permutation representation...

primitive permutation groups are transitive, not all transitive permutation groups are primitive. The simplest example is the Klein four-group acting on...

a permutation of the labels 1 to 48, depending on the position of each facet. Using this representation, the solved cube is the identity permutation which...

University of Leeds where he specialises in mathematical logic, infinite permutation groups, homogeneous structures and model theory. Truss began his career as...

In mathematics, a Frobenius group is a transitive permutation group on a finite set, such that no non-trivial element fixes more than one point and some...

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...

groups states that every finite simple group is cyclic, or alternating, or in one of 16 families of groups of Lie type, or one of 26 sporadic groups....

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...