Theorem 1 (the bounds): finite groups with $|\mathrm{Sym}^+(C)|\le\max\{d,2d-4\}$ and $|\mathrm{Sym}(C)|\le2d$

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Theorem 1 (the bounds): finite groups with $|\mathrm{Sym}^+(C)|\le\max\{d,2d-4\}$ and $|\mathrm{Sym}(C)|\le2d$ · Prove2Me