On Ore’s Theorem and Universal Words for Permutations and Injections of Infinite Sets
نویسندگان
چکیده
We give a simple proof that any injective self-mapping of an infinite set M can be written as a product of an injection and a permutation of M both having infinitely many infinite orbits (and no others). This implies Ore’s influential theorem that each permutation of M is a commutator, a similar result due to Mesyan for the injections of M , and a result on which injections f of M can be written in the form f = x · y.
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