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12.63 (1992)

Open

Does there exist a soluble permutation group of infinite degree that has only finitely many orbits on triples? Conjecture: No.

Contributor: P. M. Neumann

Progress

Comment of 2001: It is proved (D. Macpherson, in: Advances in algebra and model theory (Algebra Logic Appl., 9), Gordon & Breach, Amsterdam, 1997, 87–92) that every infinite soluble permutation group has infinitely many orbits on quadruples.

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