In mathematics, an

**alternating group**is the**group**of even permutations of a finite set. The**alternating group**on a set of n elements is called the**alternating group**of degree n, or the**alternating group**on n letters and denoted by A_{n}or Alt(n).Consequently, is d3 an Abelian group?

A non-

**Abelian group**, also sometimes known as a noncommutative**group**, is a**group**some of whose elements do not commute. The simplest non-**Abelian group**is the dihedral**group D3**, which is of**group**order six.Is a3 cyclic?

For example

**A3**is a normal subgroup of S3, and**A3**is**cyclic**(hence abelian), and the quotient group S3/**A3**is of order 2 so it's**cyclic**(hence abelian), and hence S3 is built (in a slightly strange way) from two**cyclic**groups. More generally: Definition 1.What is the symmetric group?

In abstract algebra, the

**symmetric group**defined over any set is the**group**whose elements are all the bijections from the set to itself, and whose**group**operation is the composition of functions. For the remainder of this article, "**symmetric group**" will mean a**symmetric group**on a finite set.