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    Left Cosets of Z in Q

    Homework Statement View Z as a subgroup of the additive group of rational numbers Q. Show that given an element \bar{x} \in Q/Z there exists an integer n \geq 1 such that n \bar{x} = 0. Homework Equations The Attempt at a Solution As we are working in an additive group, it is...
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    Abstract Algebra Problem

    Homework Statement Let A be an abelian group, written additively, and let n be a positive integer such that nx=0 for all x \in A. Such an integer n is called an exponent for A. Assume that we can write n=rs, where r, s are positive relatively prime integers. Let A_{r} consist of all x \in A...
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