Atomic property of the fundamental groups of the Hawaiian earring and wild locally path-connected spaces

Abstract

We strengthen previous results on the fundamental groups of the Hawaiian earring and wild Peano continua. Let $X$ be a path-connected, locally path-connected, first countable space which is not locally semi-simply connected at any point. If the fundamental group $\pi_1(X)$ is a subgroup of a free product $*_{j \in J}H_j$, then it is contained in a conjugate subgroup to some $H_j$.