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In mathematics, the notion of permutation relates to the act of arranging all the members of a set into some sequence or order, or if the set is already ordered, rearranging (reordering) its elements, a process called permuting.s another example, an anagram of a word, all of whose letters are different, is a permutation of its letters. In this example, the letters are already ordered in the original word and the anagram is a reordering of the letters.
The operation with respect to which a group is defined is often called the group operation, and a set is said to be a group under this operation. Elements, , , ... with binary operation between and denoted form a group if. 1. Closure: If and are two elements in, then the product is also in. 2. basic example of a finite group is the symmetric group, which is the group of permutations (or under permutation) of objects. The simplest infinite group is the set of integers under usual addition. For continuous groups, one can consider the real numbers or the set of invertible matrices.