Analogues of Nielsen’s and Magnus’s theorems for free Burnside groups of period 3 (Նիլսենի և Մագնուսի թեորեմների անալոգները ազատ բեռնսայդյան խմբերի համար

Аннотация

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 Fm of rank m. We show that the kernel of the natural homomorphism Aut(B(2,3)) → GL2(Z3) is the group of inner automorphisms of B(2,3).