Alternating group

The alternating group on a finite set $M$ is the group of even permutations on the set $M$ ; it is denoted $A_M$ , $\mathfrak{A}_M$ , or $\text{Alt}(M)$ . When $M = \{1, \dotsc, n\}$ , this group is denoted $A_n$ , $\mathfrak{A}_n$ , or $\text{Alt}(n)$ . This is a normal subgroup of the symmetric group; and for $n=3$ or $n\ge 5$ , it is in fact a simple group.

$A_n$ is also the group of determinant-preserving permutations of the rows of an $n \times n$ matrix.

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Alternating group

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