On solvable groups of finite Morley rank

Nesin, Ali

doi:10.1090/S0002-9947-1990-0968420-2

On solvable groups of finite Morley rank
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by Ali Nesin

Trans. Amer. Math. Soc. 321 (1990), 659-690

DOI: https://doi.org/10.1090/S0002-9947-1990-0968420-2

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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 ${\mathbf {Z}}[T]/\text {ann}G’$ is intepretable in $G$. We exploit the methods used in proving these results to find more information about solvable groups.

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