We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
This journal utilises an Online Peer Review Service (OPRS) for submissions. By clicking "Continue" you will be taken to our partner site https://ef.msp.org/submit_new.php?jpath=cms_cmb. Please be aware that your Cambridge account is not valid for this OPRS and registration is required. We strongly advise you to read all "Author instructions" in the "Journal information" area prior to submitting.
It was claimed by Halmos in 1944 that if 
$G$ is a Hausdorff locally compact topological abelian group and if the character group of $G$ is torsion free, then $G$ is divisible. We prove that such a claim is false by presenting a family of counterexamples. While other counterexamples are known, we also present a family of stronger counterexamples, showing that even if one assumes that the character group of $G$ is both torsion free and divisible, it does not follow that $G$ is divisible.