## Permutations

Suppose is a finite set having distinct elements. Then a one-one mapping of onto itself is called a permutation of... Click here to read more

From basic to higher mathematics

Suppose is a finite set having distinct elements. Then a one-one mapping of onto itself is called a permutation of... Click here to read more

Two permutations and of degree are said to be equal if we have , . Example: If and are... Click here to read more

If is a permutation of degree such that replaces each element by the element itself, is called the identity permutation... Click here to read more

The products or composite of two permutations and of degree denoted by is obtained by first carrying out the operation... Click here to read more

If is a permutation of degree , defined on a finite set consisting of distinct elements, by definition is a... Click here to read more

Let be a permutation on a set . If a relation is defined on such that for some integrals ,... Click here to read more

A permutation of the type is called a cyclic permutation or a cycle. It is usually denoted by the symbol... Click here to read more

Theorem 1: The product of disjoint cycles is commutative. Proof: Let and be any two disjoint cycles, i.e. there is... Click here to read more

The set of all permutations on symbols is a finite group of order with respect to the composite of mappings... Click here to read more

A permutation is said to be an even permutation if it can be expressed as a product of an even... Click here to read more

Suppose is a group and the composition has been denoted by multiplicatively, let . Then by closure property etc., are... Click here to read more

If is a group and is an element of group , the order (or period) of is the least positive... Click here to read more

Theorem 1: The order of every element of finite group is finite. Proof: Let be a finite group and let... Click here to read more

A group is called a cyclic group if, for some , every element is of the form , where is... Click here to read more

Theorem 1: Every cyclic group is abelian. Proof: Let be a generator of a cyclic group and let for any... Click here to read more