ANALOGUES OF NIELSEN'S AND MAGNUS'S THEOREMS FOR FREE BURNSIDE GROUPS OF PERIOD 3

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ANALOGUES OF NIELSEN'S AND MAGNUS'S THEOREMS FOR FREE BURNSIDE GROUPS OF PERIOD 3 Hayk Aslanyan

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).

DOI: 10.46991/PYSU:A/2017.51.3.217 Physical and Mathematical Sciences, 51(3 (244) 217-223

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Keywords

Nielsen automorphism, Magnus’s property, tame automorphism, free Burnside group, free group

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