Bijectivity of the skew map in $n$-groups

A number of problems connected with the skew map $h\colon x\to\bar{x}$ in an $n$-group is considered. In this paper some $n$-groups where $h\colon x\to\bar{x}$ and ${}^{(t)}\colon x\to x^{(t)}$ are automorphisms or bijective maps are indicated.