Strongly imbedded infinitely isolated subgroup of a periodic group

Characterization of the groupsSL 2 (K) andSz(K) over a locally finite fieldK of characteristics 2

“…As shown in [2], O~S~ is finite since ~BCS~ + { ; from here and from the theorem of [2] we obtain a contradiction with the existence of the element $ . As shown in [2], O~S~ is finite since ~BCS~ + { ; from here and from the theorem of [2] we obtain a contradiction with the existence of the element $ .…”

“…By Lemma 2.1, M~4=~ and, consequently, N is strongly imbedded in K. By Lemma 2.6, K is a finite subgroup; therefore, if N contains more than one involution, then, by the theorem from[2], ~ satisfies the assertion ofTheorem 2.2, in spite of our assumption. Obviously, L~_-gr(~'~d'~-'c"]~L c andl/tl= ILJ; ¢ The lemma is proved.consequently, 0J e N~L ~ .As the fundamental step of the proof, we show that ~ satisfies the assertion of Theorem 2.2.…”

“…If ~ is some involu- In order to avoid misunderstandings, we mention that in Lemma 1 of [2] one states " any subgroup of 0~ of order p~, where p and ~ are not necessarily distinct prime numbers, is cyclic," while in [i] A particular case of the theorem from [2] has been communicated in [4]. Now we obtain a generalization of the fundamental result of [2], needed in the sequel. which contradicts the assumption of the lemma.…”