Decomposable involution centralizers involving exceptional lie type simple groups

There have been investigations (Janko (1966), Janko and Thompson (1966), Yamaki (1972)) of finite groups G which contain a central involution t whose centralizer (in G) has the form C(t) = 〈t〉 × F, where F is isomorphic to a non-abelian simple group. Here it is shown such a group cannot be simple when F is isomorphic to an exceptional Lie type simple group of odd characteristic. Specifically the following theorem is proved.