5.19 (1976)

a) Let $G$ be an infinite locally finite simple group satisfying the minimum condition for 2-subgroups. Is $G = \text{PSL}_2(F)$, $F$ some locally finite field of odd characteristic, if the centralizer of every involution of $G$ is almost locally soluble?
b) Can one characterize the simple locally finite groups with the min-2 condition containing a maximal radical non-trivial 2-subgroup of rank $\leqslant 2$ as linear groups of small rank?