most recent 30 from http://mathoverflow.net 2013-05-22T03:56:04Z http://mathoverflow.net/feeds/user/2616 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/17295/results-about-the-order-of-a-group-forcing-a-particular-property Adam Libster 2010-03-06T17:07:48Z 2010-03-06T18:30:47Z

<p>Given a group of order $n$ where $n$ is either a specific number, or a number of a particular form, e.g. square-free, when does $n$ completely determine a particular group property among all groups of that order? Vipul's group theory wiki has several stubs on this topic, and in the language of his wiki, I will call this a $P$-forcing number, where $P$ is a particular group theoretic property.</p> <p>We already have quite a few easy examples, for instance, orders $pq$, $pqr$, and $p^2q$ force solvability, and $p^2$ forces abelian. Then there are more specific results like 99 is an abelian-forcing number.</p> <p>I am interested in general, in any results of this flavor beyond what would be considered a common result in a standard graduate-level group theory book.</p>

http://mathoverflow.net/questions/13897/uses-of-the-holomorph-holg-g-rtimes-autg Adam Libster 2010-02-03T00:52:09Z 2010-02-03T14:01:07Z

<p>In every group theory textbook I've read, the holomorph has been defined, and maybe a few problems done with it. I've also seen papers focusing on computing Hol($G$) for a specific class of $G$.</p> <p>One thing I have never seen is any actual use for it. Are there major results using the holomorph of a group? Does it occur in the proof of any useful theorems? </p> <p>It seems intrisically interesting to me since it allows you to treat automorphisms of a group and elements of a group uniformly, and I would definitely like to learn more about it.</p>

http://mathoverflow.net/questions/8216/less-elementary-group-theory/9093#9093 Adam Libster 2009-12-16T09:27:12Z 2009-12-16T09:27:12Z

<p>I'm going to first re-recommend Robinson's Course in the Theory of Groups. There are many interesting branches of group theory like geometric group theory that tie into other subjects, but you should probably make sure you know group theory proper first. And the only real way to know what topics are important is to get a book.</p>

http://mathoverflow.net/questions/18716/sylow-subgroups Adam Libster 2010-03-19T21:31:14Z 2010-03-19T21:31:14Z

Victor, if you haven't studied finite solvable groups in depth yet, you should look at how Hall subgroups generalize the sylow's theorems for finite solvable groups by extending the results from p-groups to pi-groups.

http://mathoverflow.net/questions/14684/almost-but-not-quite-a-homomorphism Adam Libster 2010-02-10T09:07:43Z 2010-02-10T09:07:43Z

Vipul - I just want to say that I love the group properties wiki and I use it all the time!

http://mathoverflow.net/questions/13897/uses-of-the-holomorph-holg-g-rtimes-autg/13974#13974 Adam Libster 2010-02-04T08:11:25Z 2010-02-04T08:11:25Z

Yeah I'd definitely appreciate some references if you wouldn't mind.

http://mathoverflow.net/questions/12638/taking-lecture-notes-in-lectures/12673#12673 Adam Libster 2010-02-03T08:27:44Z 2010-02-03T08:27:44Z

I don't get it, if you're going to type it up, wouldn't it be faster just to write it unformatted in notepad and then tex it?