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4.27 (1973)

Solved

Describe all finite simple groups $G$ which can be represented in the form $G = ABA$, where $A$ and $B$ are abelian subgroups.

Contributor: I. P. Doktorov

Progress

They are described mod CFSG (D. L. Zagorin, L. S. Kazarin, Dokl. Math., 53, no. 2 (1996), 237–239; D. L. Zagorin, Some problems of ABA-factorizations of permutation groups and classical groups (Cand. Diss.), Yaroslavl’, 1994 (Russian); D. L. Zagorin, L. S. Kazarin, Problems in algebra, Gomel’ Univ., Gomel’, no. 11 (1997), 27–41 (Russian); E. P. Vdovin, Algebra and Logic, 38, no. 2 (1999), 67–83).

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