High Quality Content by WIKIPEDIA articles! In model theory, a stable group is a group that is stable in the sense of stability theory. An important class of examples is provided by groups of finite Morley rank (see below).The Cherlin–Zilber conjecture, due to Gregory Cherlin (1979) and Boris Zilber (1977), suggests that infinite (?-stable) simple groups of finite Morley rank are simple algebraic groups over algebraically closed fields. The conjecture would have followed from Zilber trichotomy conjecture. Cherlin posed the question for all ?-stable simple groups, but remarked that even the case of groups of finite Morley rank seemed hard.

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