Normal automorphisms of the metabelian product of free abelian Lie algebras

Let M be the metabelian product of free abelian Lie algebras of finite rank. In this study we prove that every normal automorphism of M is an IA-automorphism and acts identically on M′.

NORMAL AUTOMORPHISMS OF FREE BURNSIDE GROUPS OF LARGE ODD EXPONENTS

Let [Formula: see text] be a free Burnside group of a sufficiently large odd exponent n with a basis [Formula: see text] of cardinality at least 2. We prove that every normal automorphism of [Formula: see text] is inner. We also prove that a free Burnside group of large odd exponent n can be normally embedded into group of exponent n only as a direct factor.