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16.85 (2006)

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Suppose that groups $G, H$ act faithfully on a regular rooted tree by finite-state automorphisms. Can their free product $G * H$ act faithfully on a regular rooted tree by finite state automorphisms?

See the definitions in (R. I. Grigorchuk, V. V. Nekrashevich, V. I. Sushchanskiĭ, Proc. Steklov Inst. Math., 2000, no. 4 (231), 128–203).

Contributor: V. I. Sushchanskiĭ

Progress

Yes, it can (M. Fedorova, A. Oliynyk, Algebra Discrete Math., 23, no. 2 (2017), 230–236).

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