Title: On Strong Small Loop Transfer Spaces Relative to Subgroups of Fundamental Groups,
Abstract: Let $H$ be a subgroup of the fundamental group $\pi_{1}(X,x_{0})$. By
extending the concept of strong SLT space to a relative version with respect to
$H$, strong $H$-SLT space, first, we investigate the existence of a covering
map for strong $H$-SLT spaces. Moreover, we show that a semicovering map is a
covering map in the presence of strong $H$-SLT property. Second, we present
conditions under which the whisker topology agrees with the lasso topology on
$\widetilde{X}_{H}$. Also, we study the relationship between open subsets of
$\pi_{1}^{wh}(X,x_{0})$ and $\pi_{1}^{l}(X,x_{0})$. Finally, we give some
examples to justify the definition and study of strong $H$-SLT spaces.