From 26cf156763f71aaa9f638408ba4bffb85b886ab0 Mon Sep 17 00:00:00 2001
From: Simon-Kor <52245124+Simon-Kor@users.noreply.github.com>
Date: Sat, 31 Aug 2024 18:02:42 +0200
Subject: working commit

---
 library/algebra/group.tex | 10 ++++++++++
 1 file changed, 10 insertions(+)

(limited to 'library/algebra/group.tex')

diff --git a/library/algebra/group.tex b/library/algebra/group.tex
index a79bd2f..7de1051 100644
--- a/library/algebra/group.tex
+++ b/library/algebra/group.tex
@@ -80,3 +80,13 @@
 \begin{definition}\label{group_automorphism}
     Let $f$ be a function. $f$ is a group-automorphism iff $G$ is a group and $\dom{f}=G$ and $\ran{f}=G$. 
 \end{definition}
+
+\begin{definition}\label{trivial_group}
+    $G$ is the trivial group iff $G$ is a group and $\{\neutral[G]\}=G$.
+\end{definition}
+
+\begin{theorem}\label{trivial_implies_abelian}
+    Let $G$ be a group.
+    Suppose $G$ is the trivial group.
+    Then $G$ is an abelian group.
+\end{theorem}
-- 
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