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This is a right-topological semigroup consisting of all maximal linked systems on $X$ endowed with the operation $$\\mathcal A\\circ\\mathcal B=\\{C\\subset X:\\{x\\in X:x^{-1}C\\in\\mathcal B\\}\\in\\mathcal A\\}$$ that extends the group operation of $X$. We characterize right zeros of $\\lambda(X)$ as invariant maximal linked systems on $X$ and prove that $\\lambda(X)$ has a right zero if and only if each element of $X$ has odd order. 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