I am looking for an example for such a module, because I want to find a module for which the set of torsion elements is not a submodule of $M$.
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Would $\Bbb Z/6\Bbb Z$ suffice? – Angina Seng Jun 22 '17 at 15:28
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As a module over itself? – Angina Seng Jun 22 '17 at 15:35
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You ask two seemingly unrelated questions. Lord Shark the Unknown provided an answer to the thread's header. On the other hand, https://math.stackexchange.com/questions/1939173/torsion-elements-do-not-form-a-submodule answers the thread's main question. – Batominovski Jun 22 '17 at 15:35
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thanks for boths answers! – MPB94 Jun 22 '17 at 15:36