Factors with prescribed number of invariant subalgebras not arising from subgroups

Yongle Jiang, Qinxuan Xu

For any given integer $n\ge 1$, we construct i.c.c. groups $G$ such that the II${}_1$ factors $L(G)$ have exactly $n$-many $G$-invariant von Neumann subalgebras not arising from sub…