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14.69 (1999)

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For every finite simple group find the minimum of the number of generating involutions satisfying an additional condition, in each of the following cases.
$\qquad$ a) The product of the generating involutions equals 1.
$\qquad$ b) (Malle–Saxl–Weigel). All generating involutions are conjugate.
$\qquad$ c) (Malle–Saxl–Weigel). The conditions a) and b) are simultaneously satisfied.
$\qquad$ d) All generating involutions are conjugate and two of them commute.

Contributor: Ya. N. Nuzhin

Progress

Editors' comment (on part c): partial progress was obtained in (J. Ward, PhD Thesis, QMW, 2009, http://www.maths.qmul.ac.uk/~raw/JWardPhD.pdf).

Editors' comment (on part a): These numbers are found (R. I. Gvozdev, Ya. N. Nuzhin, Siberian Math. J., 64, no. 6 (2023), 1160–1171; M. A. Vsemirnov, R. I. Gvozdev, Ya. N. Nuzhin, Abstracts of Int. Conf. Mal'cev Meeting 2023, Novosibirsk, 2023, p. 148).

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