Element Commutes with Square in Group/Proof 1
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Theorem
Let $\left({G, \circ}\right)$ be a group.
Let $x \in G$.
Then $x$ commutes with $x \circ x$.
Proof
\(\ds x \circ \paren {x \circ x}\) | \(=\) | \(\ds \paren {x \circ x} \circ x\) | Group Axiom $\text G 1$: Associativity |
$\blacksquare$
Sources
- 1968: Ian D. Macdonald: The Theory of Groups ... (previous) ... (next): $\S 1$: Some examples of groups