... decompositions of the ncycles ρ1 and ρ2 In the proof of the theorem itself, it is first noted that the theorem holds for n = The proof proceeds by induction Given an element σ ∈ An+ 1 , the alternating ... [31], theorem 7)) For n ≥ 5, every element of the alternating group An is a simple commutator of elements of An The authors Ellers and Gordeev, in “On the Conjectures of J Thompson and O Ore ... ALGORITHMIC INVESTIGATION OF THE SIMPLE COMMUTATOR PROMISE PROBLEM by James Ulrich Advisor: Professor Michael Anshel Motivated by a desire to test the security of the pubic key exchange protocol of I Anshel,...