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Divisibility By |G| For Powers Of Ordered K-Sets, Jeffery Vanderkam
Divisibility By |G| For Powers Of Ordered K-Sets, Jeffery Vanderkam
Mathematical Sciences Technical Reports (MSTR)
It is shown that the number of ordered k-sets of a group G whose nth power contains exactly i elements is always a multiple of IGI. An elementary proof of the fact that the number of ordered pairs ( x , y ) such that x2 = y2 is equal to kr lGI is also given.