On Characterization of Simple Orthogonal Groups of Odd Dimension in the Class of Periodic Groups

Siberian Mathematical Journal - Suppose that $ n $ is an integer, $ n\geq 3 $ . We prove that a periodic group saturated with a set of the finite simple groups $ O_{2n+1}(q) $ , where $ q $ is...     

On groups with given properties of the finite subgroups generated by couples of 2-elements

Suppose that every finite subgroup, generated by a couple of 2-elements of a periodic group, is either nilpotent of class 2 or of exponent 4. We prove that the group possesses the normal Sylow 2-subgroup that is either nilpotent of class 2 or of exponent 4.     

Bioactive materials for bone regeneration based on zinc-modified hydroxyapatite

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Periodic groups generated by a pair of virtually quadratic automorphisms of an abelian group

The finiteness is proven of a periodic group generated by a pair of virtually quadratic automorphisms of an abelian group.     

On local finiteness of some groups of period 12

The local finiteness is proven of all groups of period 12 in which the order of the product of every two involutions is at most 4.     

On the periodic groups saturated by direct products of finite simple groups

We prove the local finiteness of a periodic group G saturated by direct products of an elementary abelian 2-group of fixed order and the simple groups L ₂(q) under condition that G contains an element of order 4.     

On the periodic groups saturated by direct products of finite simple groups. II

We continue the study that was started in [1] of periodic groups saturated with direct products of elementary abelian 2-groups and simple linear groups of dimension 2.     

Infinite Groups Containing a Proper Hughes Subgroup H3(G)

Algebra and Logic - We consider groups in which H3(G) is both nontrivial and proper. In particular, it is proved that in such a group, |G : H3(G)| = 3.     

Characterization of Locally Finite Simple Groups of the Type <Superscript>3</Superscript><Emphasis Type="Italic">D</Emphasis><Subscript>4</Subscript> Over Fields of Odd Characteristic in the Class of Periodic Groups

We prove that a periodic group is locally finite, given that each finite subgroup of the group lies in a subgroup isomorphic to a finite simple group of Lie type ³D₄ over a field of odd characteristic.