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Alternating group

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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.

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Looking for a challenging algebra text? Preparing for MATHCOUNTS or the AMC exams?
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