As according to Cayley's theorem "Every group is isomorphic to a subgroup of some symmetric group". Now my question is: the additive group of real numbers is isomorphic to which permutation group...
2026-04-01 13:12:48.1775049168
Cayley's theorem
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The answer is unfortunately not interesting. A permutation $\pi$ of the real line is called a translation if there exists a real number $a$ such that $\pi(x)=x+a$ for all $x$. The translations form a subgroup of the permutation group of $\mathbb{R}$, and this subgroup is isomorphic to the reals under addition.