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elements of A5

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elements of A5

how does one determine how many elements of a certain order there are in A5 the even permutation group? thanks!


Here is the strategy to find, the number of subgroups of a given order say [;m;] of [;A_n;]. I do not know whether there is a closed form, but the following can be implemented as a algorithm on the computer.

1. First verify the possibility by writing down a cycle structure (disjoint cycles)for such an operation. Remember that [;lcm;] of the lengths of the cycles should give [;m;] and the number of transpositions should be even.

2. Taking care of possible automorphisms, we can map every element in a cycle to another element, thus a stirling number with certain correction.

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