Half-automorphism group of a class of Bol loops

A Bol loop is a loop that satisfies the Bol identity $(xy\mathrm{.}z)y=x(yz\mathrm{.}y)$. If $L$ is a loop and $f:L\to L$ is a bijection such that $f(xy)\in \{f(x)f(y),f(y)f(x)\}$, for every $x$, $y\in L$, then $f$ is called a half-automorphism of $L$. In this paper, we describe the half-automorphism group of a class of Bol loops of order $4m$.