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The algebraicity conjecture for simple groups of finite Morley rank, also known as the Cherlin–Zil'ber conjecture, states that simple groups of finite Morley rank are simple algebraic groups over algebraically closed fields. In the last fifteen years, the main line of attack on this problem has been Borovik's program of transferring methods from finite group theory, which has led to considerable progress; however, the conjecture itself remains completely open. In Borovik's program, groups of finite Morley rank are divided into four types, odd, even, mixed, and degenerate, according to the structure of their Sylow 2-subgroup. For  even  and  mixed type  the algebraicity conjecture has been proven.

Sylow theory for p = 0 in solvable groups of finite Morley rank