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Brandon Rozek 2023-01-18 11:50:40 -05:00
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@ -1,5 +1,5 @@
---
title: "Groups Simplified"
title: "Simplifying the Definition of Algebraic Groups"
date: 2019-12-10T21:40:00-05:00
draft: false
tags: [ "Math" ]
@ -15,7 +15,12 @@ Let us have a set $G$ together with a binary operation $*$. We will use multipli
2. $ex = x$
3. $x^{-1} x = e$
for some fixed $e \in G$, then we say that $\langle G, * \rangle$ is a group. In class, we needed to show that $xe = x$ and $xx^{-1} = e$. However, these can be derived by the prior properties.
for some fixed $e \in G$, then we say that $\langle G, * \rangle$ is a group.
When I was taking Abstract Algebra, we needed to also show that $xe = x$ and $xx^{-1} = e$ for an algebraic structure to be a group.
However, these can be derived by the prior properties.
### Prove $xx^{-1} = e$
\begin{align*}