11.12 (1990)

a) Suppose that $G$ is a simple locally finite group in which the centralizer of some element is a linear group, that is, a group admitting a faithful matrix representation over a field. Is $G$ itself a linear group?
b) The same question with replacement of the word “linear” by “finitary linear”. A group $H$ is finitary linear if it admits a faithful representation on an infinite-dimensional vector space $V$ such that the residue subspaces $V(1 - h)$ have finite dimensions for all $h \in H$.