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 π₁(X) is a subgroup of a free product *_{j ∈ J}H_j, then it is contained in a conjugate subgroup to some H_j.