Let $G$ be a non-trivial torsion-free Abelian group. If $T$ is a maximal free subgroup of $G$, then $G\over T$ is periodic?
How can we prove this?
Maximal Free Subgroups and Torsion
3
$\begingroup$
abstract-algebra
group-theory
free-groups
1 Answers
0
Show that if a coset $gT$ has infinite order in the factor group then $\langle g,T\rangle$ is a free-abelian subgroup of $G$ with proper subgroup $T$, contrary to the hypothesis on maximality of $T$.
-
0Perfect! Tha$n$ks you too! Now it's all clear :D (at least for now) – 2012-10-05