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6.6 (1978)

Solved

Let $P, Q$ be permutation representations of a finite group $G$ with the same character. Suppose $P(G)$ is a primitive permutation group. Is $Q(G)$ necessarily primitive?

Contributor: H. Wielandt

Progress

No, not necessarily (mod CFSG) (R. M. Guralnick, J. Saxl, in: Groups, Combinatorics, Geometry, Proc. Durham, 1990, Cambridge Univ. Press, 1992, 364–367).

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