Category Archives: Group theory

The Baer-Specker Group

Posted on July 2, 2014 by Jeremy Brazas

One of the infinite abelian groups that is important to infinite abelian group theory and which has shown up naturally in previous posts on infinitary fundamental groups is the Baer-Specker group, often just called the Specker group. This post isn’t … Continue reading →

Posted in Baer-Specker group, earring group, earring space, Free abelian groups, Free groups, Group homomorphisms, Infinite Group Theory | Tagged , , , , , , , | 8 Comments

Homomorphisms from the harmonic archipelago group to finite groups

Posted on June 8, 2014 by Jeremy Brazas

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

Homomorphisms from the earring group to finite groups

Posted on June 7, 2014 by Jeremy Brazas

One of the the surprising things about the earring group (the fundamental group of the earring space ) is that the group of homomorphisms to the additive group of integers is countable (see this post for details) even though is … Continue reading →

Posted in earring group, earring space, Finite groups, Fundamental group, Group homomorphisms, Ultrafilter | Tagged , , , , , , , , , , , , | 1 Comment