## Group Theory

Unfortunately, abstract algebra is not typically part of the ECE/CS curriculum. Here is a very brief overview/review of the group theoretic concepts involved in the 3-25-10 and 3-30-10 lectures.

A group is a set $G$ along with a binary operation $\cdot$ under which the set is closed such that the following group axioms hold.

  1. The operation is associative
2. There is an identity element: $\exists e\in G$ s.t. $x\cdot e = e\cdot x = x ~~\forall x\in G$
3. Each element has an inverse: $\forall x\in G ~~ \exists x^{-1}\in G$ s.t. $x\cdot x^{-1} = x^{-1}\cdot x = e$


One particularly useful example is the Symmetric Group.

An important concept in the 3-25-10 and 3-30-10 lectures is that of a Group Action.

--Jvaught 20:38, 30 March 2010 (UTC)

## Alumni Liaison

Prof. Math. Ohio State and Associate Dean
Outstanding Alumnus Purdue Math 2008

Jeff McNeal