Real Elements in Spin Groups

Let $F$ be a field of characteristic $\mathrm{\ne }2$. Let $G$ be an algebraic group defined over $F$. An element $t\in G(F)$ is called {\bf real} if there exists $s\in G(F)$ such that $st{s}^{-1}=t^{-1}$. A semisimple element $t$ in $GL_n(F), SL_n(F), O(q), SO(q), Sp(2n)$andthegroupsoftype$G_2$over$F$ is real if and only if $t={\tau }_1{\tau }_2$ where ${\tau }_1^2=\pm 1={\tau }_2^2$ (ref. \cite{st1,st2}). In this paper we extend this result to the semisimple elements in $Spin$ groups when $\dim (V)\equiv 0,1,2\text{imod}4$.