Linear representations of soluble groups of finite Morley rank

Tuna Altinel (1) , John S. Wilson (2)

1 AGL - Algèbre, géométrie, logique
2 University College, Oxford

Sufficient conditions are given for groups of finite Morley rank having non-trivial 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. On 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.

Domaines: Théorie des groupes [math.GR]; Logique [math.LO]

Tuna Altinel, John S. Wilson. Linear representations of soluble groups of finite Morley rank. Proceedings of the American Mathematical Society, 2011, 139 (8), pp.2957-2972. ⟨hal-00943775⟩