Free nonassociative supercommutative algebras

In the present work, we prove that homogeneous subalgebras of free nonassociative supercommutative algebras are free. As a consequence, we show that the group of automorphisms of a free nonassociative supercommutative algebra of finite rank is generated by elementary automorphisms. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 3, pp. 103–109, 2003.