Power-conjugate equations in symmetric groups
Power-conjugate equations in symmetric groups
AbstractAbstractFirst we consider the solutions of the general “cubic” equation α1°xr1°α2°xr2°α3°xr3=1 (with r1,r2,r3∈{1,−1}) in the symmetric group Sn. In certain cases this equation can be rewritten as α°y°α−1=y2 or as α°y°α−1=y−2, where α∈Sn depends on the αi’s and the new unknown permutation y∈Sn is a product of x (or x−1) …