Dummit and Foote Section 2.1 (Definitions and Examples of Subgroups) Exercise 6 reads as follows:

Let G be an abelian group. Prove that H = {g $\displaystyle \in$ G| |g| is less than infinity} is a subgroup of G (called the torsion subgroup of G). Give an explicit example where this set is not a subgroup when G is not abelian.

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H = {g $\displaystyle \in$ G| |g| is less than infinity}

Let x,y $\displaystyle \in $ H ie |x| is less than infinity and |y| is less than infinity

Need to show x$\displaystyle y^{-1}$ $\displaystyle \in$ H

ie need to show |x$\displaystyle y^{-1}$| is less than infinity

? but how does one do this? Also ? explicit example ?

Can anyone help?

Peter