Tag Archives: hom-set

Homomorphisms from the harmonic archipelago group to finite groups

This post is a brief application of a result discussed in the last post about the existence of odd ways to map the fundamental group of the Hawaiian earring onto an arbitrary finite group : Theorem 1: Let be any non-trivial finite group and be a loop … Continue reading

Posted in Cardinality, Finite groups, Fundamental group, harmonic archipelago | Tagged , , , , , | Leave a comment

The earring group is not free (Part II)

This post is Part II in an explanation of why the fundamental group of the earring space is not a free group. I’ll be referencing the notation and results that we worked through in Part I. Recall that the earring group  is … Continue reading

Posted in earring group, earring space, Free groups, Fundamental group, Group homomorphisms | Tagged , , , , , , | 5 Comments