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Theorem 1 answers the question formulated by Ya.N.Nuzhin [1, question 15.67] for the group G2(Z) : What adjoint Chevalley groups over the ring of integers are generated by three involutions, two of which commute? This problem has not been solved. We just know that groups SLn(Z), n > 14 are generated by three involutions, two of which commute [2]. Groups PSLn(Z) are generated by three involutions, two of which commute when n > 5 [3]. Note also that adjoint Chevalley group B2(Z) is not generated by three involutions, two of which commute. It follows from the fact that group PSp4(3) is not generated by three involutions, two of which commute [4].

Generation of the Chevalley Group of Type G2 over the Ring of Integers by Three Involutions Two of which Commute