I’m sitting in a course on representation theory this semester and though it will primarily deal with finite groups I’m extremely excited! The professor is very good, very clear and motivates material very well. The past few days has been a review of basic group theory but today a few nice items came up I wanted to share.
I’ve known about the first isomorphism theorem for a while but I saw a lovely example of it today. Take the general linear group over an arbitrary field F then the determinant is a surjective homomorphism where F* is the field without it’s ‘addition’ identity (i.e. zero). Then the kernel of this map are those matrices with determinant a unit in F, so ! While a quotient like certainly taxes my mind, we know from the first isomorphism theorem that this is isomorphic to F*.
I’ll try to keep this blog in the loop of this class. Also I’m trying to form a reading group on campus on the Foundations of Mathematics by Kunen so with any luck I will have some posts on that as well.