ANALOGUES OF NIELSEN’S AND MAGNUS’S THEOREMS FOR FREE BURNSIDE GROUPS OF PERIOD 3 - Atabekyan, V.S.; Aslanyan, H.T.; Grigoryan, H.A.; Grigoryan, A.E. (Proceedings of the YSU A: Physical and Mathematical Sciences, 2017)
We prove that the free Burnside groups B(m,3) of period 3 and rank m≥1 have Magnus’s property, that is if in B(m,3) the normal closures of r and s coincide, then r is conjugate to s or s^-1. We also prove that any automorphism of B(m,3) induced by a Nielsen automorphism of the free group F_m of rank m. We show that the kernel of the natural homomorphism Aut(B(2,3)) → GL_2(Z_3) is the group of inner automorphisms of B(2,3).