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Transactions of the American Mathematical Society

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On solvable groups of finite Morley rank

Author: Ali Nesin
Journal: Trans. Amer. Math. Soc. 321 (1990), 659-690
MSC: Primary 03C60; Secondary 20A15, 20F16
MathSciNet review: 968420
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Abstract: We investigate solvable groups of finite Morley rank. We find conditions on $ G$ for $ G'$ to split in $ G$. In particular, if $ G'$ is abelian and $ Z(G) = 1$ we prove that $ G = G' \times T$ for some $ T$ and the ring $ {\mathbf{Z}}[T]/$ann$ G'$ is intepretable in $ G$. We exploit the methods used in proving these results to find more information about solvable groups.

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