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Let $G$ be $S_{\mathbb{N}}$, the finitary permutation (i.e. permutations withfinite support) group on positive integers $\mathbb{N}$. We prove that $G$ hasthe invariant von Neumann subalgebras rigidity (ISR, for short) property asintroduced in Amrutam-Jiang's work. More precisely, every $G$-invariant vonNeumann subalgebra $P\subseteq L(G)$ is of the form $L(H)$ for some normalsugbroup $H\lhd G$ 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 $S_{\mathbb{N}}$. This gives the firstknown example of an infinite amenable group with the ISR property.

An example of infinite amenable group with the ISR property