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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.