Group with an interesting property

Question

Let $ (G,\cdot ) $ be a group and let $ a $ be the only element of the group which has order 2. Prove that $ a\cdot x=x\cdot a,\forall x\in G $ .

@C.Falcon then find it and mark this question as a duplicate — Ben Grossmann, Dec 05 '16 at 20:35

score 5 · Accepted Answer · answered Dec 05 '16 at 20:27

5

Hint: Show that $x a x^{-1}$ has order $2$ for all $x \in G$.

answered Dec 05 '16 at 20:27

Viktor Vaughn

1 Answers1