[GAP Forum] Counting all elements in a group of a given order
Stephen Linton
sal at mcs.st-andrews.ac.uk
Thu Jul 1 21:40:55 BST 2010
Dear GAP Forum.
As has just been pointed out to me, I typed too hastily:
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> Finally, for the largest examples it might be best to factorise n into prime powers and use the Sylow subgroups to find representatives of all the conjugacy classes of elements of the appropriate prime power orders. Then, aving enumerated these elements, the number of elements of order n is simply the product.
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This is entirely incorrect, since only commuting elements of prime power orders give rise to elements of the product order. It might still be possible to do something along these lines (for instance to find elements of order 12, one might explore the centralisers of elements of order 4), but it is much less simple than I implied.
Steve
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