On groups with isolated involution

We prove that an isolated involution of an infinite group does not always belong to the preimage of the center of the quotient group by the maximal (periodic) subgroups without involution.     

Two Criteria for Nonsimplicity of a Group Possessing a Strongly Embedded Subgroup and a Finite Involution

A proper subgroup H of a group G is said to be strongly embedded if 2 (H) and 2(HH ^g) (for all ). An involution i of G is said to be finite if (for all g G). As is known, the structure of a (locally) finite group possessing a strongly embedded subgroup is determined by the theorems of Burnside and Brauer--Suzuki, provided that the Sylow 2-subgroup contains a unique involution. In this paper, sufficient conditions for the equality m ₂(G)= 1 are established, and two analogs of the Burnside and Brauer—Suzuki theorems for infinite groups G possessing a strongly embedded subgroup and a finite involution are given.     

On the existence of f-local subgroups in a group

We prove the existence of infinite subgroups with nontrivial locally finite radicals and of locally finite subgroups in the groups with almost finite almost solvable elements of prime orders and in the groups with generally finite elements.     

The <Emphasis Type="Italic">F</Emphasis>-local subgroups of the groups with a generalized finite element of order 2 or 4

We prove the existence of infinite subgroups with nontrivial locally finite radicals and of infinite locally finite subgroups in the groups with almost finite almost solvable elements of order 2 and 4 and in the groups with almost finite elements.     

Frobenius Pairs with Perfect Involutions

An involution i of a group G is said to be perfect in G if any two non-commuting involutions in i^G are conjugated by an involution in the same class. We generalize theorems of Jordan and M. Hall concerning sharply doubly transitive groups, and the Shunkov theorem on periodic groups with a finite isolated subgroup of even order. __________ Translated from Algebra i Logika, Vol. 44, No. 6, pp. 751–762, November–December, 2005.