Shunkov groups, saturated by groups l 2( PN), U 3(2 n)

Investigated are Shunkov groups, saturated by groups (projective special linear group of degree 2 over finite fields), (projective special unitary group of degree 3 over fields of odd characteristics). Arbitrary group is called a Shunkov group, if every cross section by a finite subgroup of any pair of conjugate elements of Prime order generates a finite subgroup. Under periodic part group G is the subgroup generated by all elements of finite order of G, provided that it is periodic. Presented is a series of lemmas, in which we prove that: - G contains infinitely many elements of finite order; - In G there are finite subgroups K 1 and K 2, that and, but for no group of such that ; - Sylow 2-subgroup S, group G, locally finite and for any ; - All involution of S lies in - For any with the property it follows that ; - If V is a Sylow 2-subgroup of G and, then ; - All Sylow 2-subgroups of G are conjugate; - If and, then ; - Subgroup has a periodic part, where H is a locally periodic cyclic group without involutions; - The subgroup B is embeddable in locally finite simple subgroup L group G that is isomorphic U 3 (Q), where Q is a locally finite field of characteristic 2; - If the a for arbitrary nonunit element of H0, then has a periodic part N and, where t is an involution. Based on the above lemmas, we prove the theorem: the Shunkov group saturated by multiple groups of the form, has a periodic part, is isomorphic to either, or, for suitable locally of finite fields P and Q.