University of IsfahanInternational Journal of Group Theory2251-76508220190601On free subgroups of finite exponent in circle groups of free nilpotent algebras29402220810.22108/ijgt.2017.108014.1455ENJuliane HansmannDepartment of Mathematics
University of Kiel, Germany0000-0003-0847-7631Journal Article20171115Let $K$ be a commutative ring with identity and $N$ the free nilpotent $K$-algebra on a non-empty set $X$. Then $N$ is a group with respect to the circle composition. We prove that the subgroup generated by $X$ is relatively free in a suitable class of groups, depending on the choice of $K$. Moreover, we get unique representations of the elements in terms of basic commutators. In particular, if $K$ is of characteristic $0$ the subgroup generated by $X$ is freely generated by $X$ as a nilpotent group.http://ijgt.ui.ac.ir/article_22208_1d66e7d97c7526a72c80904843cf42a7.pdf