20.16 (2022)

By Hartley’s theorem (based on CFSG), if a simple locally finite group does not contain a particular finite group as a section, then it is isomorphic to a group of Lie type over a locally finite field.
$\qquad$ a) Is the same true for an infinite definably simple locally finite group? A group is said to be definably simple if it does not contain proper definable normal subgroups.
$\qquad$ b) The same question for an infinite definably simple locally finite group with bounded derived lengths of its solvable subgroups.