\(
\def\bbN{{\mathbb N}}
\def\bbQ{{\mathbb Q}}
\def\bbR{{\mathbb R}}
\def\bbZ{{\mathbb Z}}
\def\calA{{\mathcal A}}
\def\calD{{\mathcal D}}
\def\calT{{\mathcal T}}
\def\Lim{{\operatorname{Lim}}}
\)
Homework Assignment 8
Question 1. Let $A$ be an Abelian group, and let $T\colon A\to A$ be an
automorphism thereof.
- Verify that the formula $a\wedge b:=b+T(a-b)$ defines a quandle structure on
$A$. It is called the "Alexander quandle".
- Is the Alexander quandle always the conjugation quandle within a conjugation-invariant
subset of some group $G$ (which may depend on $A$ and on $T$)?
This assignment is due on Crowdmark by the end of Thursday November 26, 2020.