A remark on groups without finite quotients

Details A remark on groups without finite quotients A remark on groups without finite quotients

2009-03-14

arxiv.org/abs/0903.2536v3

Mathematics

Group Theory

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

Scientific paper

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
$\mathbb Q*\mathbb Q$, 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 $\mathbb Z/2\mathbb Z$.

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