
Abstract Algebra Abstract Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
January 2nd, 2012, 03:03 PM  #1 
Senior Member Joined: Nov 2011 Posts: 100 Thanks: 0  Proofread / give comments on algebra solutions?
Hello all I've been writing up some solutions for problems in algebra and analysis I've been doing.. If anyone has some extra time to read through one, or more, of my solutions and give me feedback whether or not I'm missing anything, I'd be GREATLY appreciative! I will attach the file for some of the algebra solutions I have written up so far.. I'll be adding to it and editing, but I appreciate any comments as is (whether typos, more serious mistakes, or additions). Thanks! [attachment=0:380wzkmi]Algebra Problems and Solutions.pdf[/attachment:380wzkmi] 
January 5th, 2012, 08:50 AM  #2 
Senior Member Joined: Sep 2008 Posts: 150 Thanks: 5  Re: Proofread / give comments on algebra solutions?
Ok, I checked the first few; here are my comments: 1.1: Claim 1: Looks good enough, but in your proof you should replace G by N twice. (Seems to be a simple typo.) Claim 2: Good. Claim 3: That is a correct description of the orbits, but it is not very far from the definition of "orbit". In fact, one can describe the orbits very explicitly. 1.2: Claim 1: Good. Claim 2: Good. 1.3: Claim 1:Also note that as . That is not apparent! It is in fact wrong for every nonsimple group G of that order. However, the fact that can be deduced quite simply. That's how far I got for now. Maybe I have more time later. rgds Peter 
January 5th, 2012, 09:19 AM  #3 
Senior Member Joined: Nov 2011 Posts: 100 Thanks: 0  Re: Proofread / give comments on algebra solutions?
Thank you for your comments so far! 1.1 Claim 3: I realize your point, and I was worried that was the case; can you give me a hint how I might actually describe the orbits explicitly? 1.3 Claim 1: Yes, I realize that I can't just note , I was just being a bit lazy I guess! To see why it's true, one can observe the following: Recall and that , where , defined as . Let . Then for every such conjugate of . But in particular, we have that , i.e., for all , and so (since we are assuming ), we get .. I think.. Or maybe this is a better approach: Define and , where , defined as . Let . Then for every such left coset of . But in particular, we have that , i.e., for all , and so we must have . Thanks again! 
January 5th, 2012, 10:23 AM  #4  
Senior Member Joined: Sep 2008 Posts: 150 Thanks: 5  Re: Proofread / give comments on algebra solutions? Quote:
Hint 2: Take a vector of your liking and try a bit where you can map it. Hint 3: As matrices in SL_n are invertible the columnvectors form a basis. Given any basis, how can you change it, so that it makes up the columnvectors of an element of Sl_n? Quote:
 
January 5th, 2012, 10:33 AM  #5  
Senior Member Joined: Nov 2011 Posts: 100 Thanks: 0  Re: Proofread / give comments on algebra solutions? Quote:
 

Tags 
algebra, comments, give, proofread, solutions 
Search tags for this page 
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Poorly proof read book/ need help understanding the solution  restin84  Advanced Statistics  1  March 19th, 2012 03:20 PM 
proofread / give comments on analysis solutions?  watson  Real Analysis  1  January 10th, 2012 05:48 PM 
can you give a proof of this theorem please  johnmath  Abstract Algebra  3  January 10th, 2011 10:38 AM 
I need 2 solutions and my Casio ClassPad only give me 1! =(  achillida  Algebra  1  January 7th, 2008 11:00 AM 
can you give a proof of this theorem please  johnmath  Real Analysis  0  December 31st, 1969 04:00 PM 