Involutions in locally finite groups

The paper deals with locally finite groups G having an involution phi such that C-G(phi) is of finite rank. The following theorem gives a very detailed description of such groups. Let G be a locally finite group having an involution phi such that C-G(phi) is of finite rank. Then G/[G,phi] has finite rank. Furthermore, [G,phi]' contains a characteristic subgroup B such that the following hold. (1) B is a product of finitely many subgroups normal in [G,phi] isomorphic to either PSL(2,K) or SL(2,K) for sonic infinite locally finite fields K of odd characteristic. (2) [G,phi]'/B has finite rank.