%0 Journal Article %T On the Makar-Limanov, Derksen invariants, and finite automorphism groups of algebraic varieties %A Vladimir L. Popov %J Mathematics %D 2010 %I arXiv %X A simple method of constructing a big stock of algebraic varieties with trivial Makar-Limanov invariant is described, the Derksen invariant of some varieties is computed, the generalizations of the Makar-Limanov and Derksen invariants are introduced and discussed, and some results on the Jordan property of automorphism groups of algebraic varieties are obtained. %U http://arxiv.org/abs/1001.1311v3