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10.30 (1986)

Solved

Does there exist a non-right-orderable group which is residually finite $p$-group for a finite set of prime numbers $p$ containing at least two different primes? If a group is residually finite $p$-group for an infinite set of primes $p$, then it admits a linear order (A. H. Rhemtulla, Proc. Amer. Math. Soc., 41, no. 1 (1973), 31–33).

Contributor: N. Ya. Medvedev

Progress

Yes, there does (P. A. Linnell, J. Algebra, 248 (2002) 605–607).

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