SOME INFINITE GROUPS WITH STRONGLY EMBEDDED SUBGROUP

An involution i of a group G is said to be finite if |ii^g| < (unlimited) for all g (belongs to) G. Suppose that G contains a finite involution and an infinite elementary Abelian 2-subgroup S and, moreover, the normalizer H = NG(S) = S(lambda)T is strongly embedded in G and is a Frobenius group with locally cyclic complement T. It is proved that G is isomorphic to L2(Q) over a locally finite field Q of characteristic 2. In particular, part (a) of Question 10.76 raised by Shunkkov in the Kourovka Notebook is answered in the affirmative.