Linear representations of soluble groups of finite Morley rank

Altınel, Tuna; Wilson, John

doi:10.1090/S0002-9939-2010-10713-X

Linear representations of soluble groups of finite Morley rank
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by Tuna Altınel and John S. Wilson PDF

Proc. Amer. Math. Soc. 139 (2011), 2957-2972 Request permission

Abstract:

Sufficient conditions are given for groups of finite Morley rank having nontrivial torsion-free nilpotent normal subgroups to have linear representations with small kernels. In particular, centreless connected soluble groups of finite Morley rank with torsion-free Fitting subgroups have faithful linear representations. Along the way, using a notion of definable weight space, we prove that certain connected soluble groups of finite Morley rank with torsion-free derived subgroup can be embedded in groups of finite Morley rank whose Fitting subgroups have definable abelian supplements.

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