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Are all branch groups of intermediate growth just-infinite? I can't seem to find an answer to this one way or another; the question is motivated by the fact all examples of intermediate growth branch groups I know being just-infinite, and by this paper by Nekrashevych in which he constructs a family of branch groups, all but one of which are just-infinite and intermediate growth and one being neither.

This paper by Bartholdi, Grigorchuk and Sunic is my main reference on branch groups so far.

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All known branch groups of intermediate growth are just infinite. That means your question is still open.

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