A remark on groups without finite quotients

Abstract

We notice that the class of nontrivial groups without proper subgroups of finite index is not elementary, because some groups in this class, such as $\mathbb{Q}\ast \mathbb{Q}$, have ultrapowers that map homomorphically onto $\mathbb{Z}/p\mathbb{Z}$ for every prime $p$. Also, some ultrapowers of certain simple groups map homomorphically onto $\mathbb{Z}/2\mathbb{Z}$.

v3: 2 pages, completely rewritten, some remarks and 2 references removed, 1 reference added.

References in corpus (1)

• Finitely generated infinite simple groups of infinite square width and vanishing stable commutator length