Dinesh
Reputation
849
Top tag
Next privilege 1,000 Rep.
Create new tags
5 21
Impact
~20k people reached

# 202 Actions

 Mar 15 awarded Popular Question Feb 22 awarded Popular Question Apr 22 awarded Yearling Feb 26 awarded Nice Question Dec 13 awarded Caucus Sep 24 awarded Autobiographer Jul 2 awarded Curious Apr 2 awarded Yearling Mar 17 awarded Popular Question Jan 27 accepted Analog of Newton's theorem for symmetric polynomials Jan 10 awarded Popular Question Apr 2 awarded Yearling Oct 12 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. Oct 12 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! Oct 12 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 Oct 12 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 $G$" Oct 12 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 ''. Oct 12 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 <$x$,$y$> Oct 12 awarded Custodian Oct 12 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