\( \def\bbN{{\mathbb N}} \def\bbQ{{\mathbb Q}} \def\bbR{{\mathbb R}} \def\bbZ{{\mathbb Z}} \def\calA{{\mathcal A}} \def\calD{{\mathcal D}} \def\calT{{\mathcal T}} \def\Lim{{\operatorname{Lim}}} \)
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Homework Assignment 8

Question 1. Let $A$ be an Abelian group, and let $T\colon A\to A$ be an automorphism thereof.

  1. Verify that the formula $a\wedge b:=b+T(a-b)$ defines a quandle structure on $A$. It is called the "Alexander quandle".
  2. 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.