>>419 関連

選択公理と群構造が関係しているのか？ （＾＾；
https://en.wikipedia.org/wiki/Group_structure_and_the_axiom_of_choice
Group structure and the axiom of choice
(抜粋)
In mathematics a group is a set together with a binary operation on the set called multiplication that obeys the group axioms. The axiom of choice is an axiom of ZFC set theory which in one form states that every set can be wellordered.

In ZF set theory, i.e. ZFC without the axiom of choice, the following statements are equivalent:

・For every nonempty set X there exists a binary operation ・ such that (X, ・) is a group.[1]
・The axiom of choice is true.

Contents
1 A group structure implies the axiom of choice
2 The axiom of choice implies a group structure
3 A ZF set with no group structure