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More precisely, every $G$-invariant von Neumann subalgebra $P\\subseteq L(G)$ is of the form $L(H)$ for some normal sugbroup $H\\lhd G$ and in this case, $H=\\{e\\}, A_{\\mathbb{N}}$ or $G$, where $A_{\\mathbb{N}}$ denotes the finitary alternating group on $\\mathbb{N}$, i.e. the subgroup of all even permutations in $S_{\\mathbb{N}}$. 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