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In this paper we show that the cloning system construction of Skipper andZaremsky [SZ21], under sufficient conditions, gives rise to Thompson-Likegroups which are stable; in particular, these are McDuff groups in the sense ofDeprez and Vaes [DV18]. This answers a question of Bashwinger and Zaremskyposed in [BZ23] in the affirmative. We show that the von Neumann algebra of theHigman-Thompson groups, $L(V_d)$, is a prime II$_1$ factor. Our method alsoprovides evidence towards the primeness conjecture for group von Neumannalgebras associated to non-elementary acylindrically hyperbolic group byshowing a class of acylindrically hyperbolic group yield prime von Neumannalgebras.

McDuff and Prime von Neumann algebras arising from Thompson-Like Groups