On special subgroups of fundamental group

Fatemah Ayatollah Zadeh Shirazi, Fatemeh Ebrahimifar, Mohammad Ali Mahmoodi

Suppose $\alpha$ is a nonzero cardinal number, $\mathcal{I}$ is an ideal on arc connected topological space $X$, and ${\mathfrak{P}}_{\mathcal{I}}^{\alpha }(X)$ is the subgroup of ${\pi }_1(X)$ (the fi…