We give the canonical normal form for the elements of the finite or infinite alternating groups using local stationary presentation of these groups.

We give a description of the algebraic group of automorphisms of a simple finite-dimensional Lie superalgebra over an algebraically closed field k of characteristic 0, which is obtained by viewing as a module over a Levi subalgebra of its even part. As an application, we give a detailed description of the group of automorphism of the k-Lie superalgebra for a large class of commutative rings R.