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 Apr22 awarded Yearling Feb26 awarded Nice Question Dec13 awarded Caucus Sep24 awarded Autobiographer Jul2 awarded Curious Apr2 awarded Yearling Mar17 awarded Popular Question Jan27 accepted Analog of Newton's theorem for symmetric polynomials Jan10 awarded Popular Question Apr2 awarded Yearling Oct12 comment Let $x$ , $y$ be the basis of a free abelian group of rank 2, prove that $2x+3y$ and $x-y$ generate a free subgroup Exactly! That was the whole point of this question. Thanks for confirming it. Oct12 comment Let $x$ , $y$ be the basis of a free abelian group of rank 2, prove that $2x+3y$ and $x-y$ generate a free subgroup Yes. Thats what I wanted to confirm for myself. Thanks! Oct12 revised Let $x$ , $y$ be the basis of a free abelian group of rank 2, prove that $2x+3y$ and $x-y$ generate a free subgroup added 152 characters in body Oct12 comment Let $x$ , $y$ be the basis of a free abelian group of rank 2, prove that $2x+3y$ and $x-y$ generate a free subgroup Ok, apologies for an unclear question. The question verbatim from Munkres is this: "If $G$ is free abelian with basis {x,y}, show that {2x+3y,x-y} is also a basis for $G$" Oct12 comment Let $x$ , $y$ be the basis of a free abelian group of rank 2, prove that $2x+3y$ and $x-y$ generate a free subgroup Yes that's what I wrote in the question but will they 'generate' the group ? I think no. But the question in Munkres was to prove that <2x+3y> and are also a basis for ''. Oct12 comment Let $x$ , $y$ be the basis of a free abelian group of rank 2, prove that $2x+3y$ and $x-y$ generate a free subgroup @Thomas Andrews that was clear but I am saying that $2x+3y$ and $x-y$ doest span <$x$,$y$> Oct12 awarded Custodian Oct12 reviewed Approve Let $x$ , $y$ be the basis of a free abelian group of rank 2, prove that $2x+3y$ and $x-y$ generate a free subgroup Oct12 asked Let $x$ , $y$ be the basis of a free abelian group of rank 2, prove that $2x+3y$ and $x-y$ generate a free subgroup Aug25 comment Analog of Newton's theorem for symmetric polynomials By a field rational over $\mathbb{Q}$ I mean a field of the form $\mathbb{Q}(t_1,...,t_n)$ where $t_1,...,t_n$ are algebraically independent.