
Recent Posts
 Hilbert’s Basis Theorem June 18, 2017
 “One Line” Algebra Qual Problems June 17, 2017
 A good title for this blog post exists, but I don’t know what it is June 9, 2017
 Groups of order 4,312 are not simple: An application of Sylow Theory May 27, 2017
 Cauchy’s Theorem May 16, 2017
Categories
 Asymptotics (1)
 Combinatorics (3)
 Contest Math (1)
 Group Theory (3)
 Patterns (1)
 Ring and Field Theory (2)
 Uncategorized (1)
Blogs I Follow
Archives
Search
Category Archives: Group Theory
“One Line” Algebra Qual Problems
Today I’m going to try to distill some solutions to previous algebra qual problems into one sentence answers. This will likely mean that the solutions are missing details, but my hope is to be able to give a decent overview … Continue reading
Groups of order 4,312 are not simple: An application of Sylow Theory
Today we will solve a problem from Wisconsin’s 2012 Algebra Qualifying Exam. The main tools used in the problem are Sylow Theory and group actions; we will take these tools for granted, but for great introductions to each topic I would … Continue reading
Cauchy’s Theorem
The famous Lagrange’s Theorem states that, in any finite group , the order of any element divides the order of . A natural follow up to this theorem is whether or not the converse holds. That is, if divides the order of … Continue reading