Associative nil-algebras and Golod groups

Non-nilpotent, finitely generated, associative nil-algebras are studied as well as their adjoint groups and Golod groups. Solutions are given to some problems in residually finite group theory, questions posed in the Kourovka Notebook included. Supported by RFBR grant No. 03-01-00356. __________ Translated from Algebra i Logika, Vol. 45, No. 2, pp. 231–238, March–April, 2006.     

The existence off-local subgroups in a group

An infinite subgroup with nontrivial finite radical is called f-local. We study the structure of subgroups of an infinite fan (set), which contain an element of prime order not embeddable in an f-local subgroup. It is proved that f-local and infinite Abelian subgroups exist in groups under certain finiteness conditions. Supported by a grant of the Russian Federation State Committee on Higher Schools of Learning. Translated fromAlgebra i Logika, Vol. 36, No. 5, pp. 573–598, September–October, 1997.     

Groups Saturated with Finite Frobenius Groups

Mathematical Notes - In the paper, the structure of Shunkov groups and periodic groups with a finite non-Engel element that are saturated with finite Frobenius groups and contain a nontrivial...     

A group with <Emphasis Type="Italic">H</Emphasis>-Frobenius element of even order

We settle Question 10.61 in the Kourovka Notebook for the case where the order of an element a is even.Supported by RFBR grant No. 03-01-00356 and by the Krasnoyarsk Science Foundation, project 11F0202C.Translated from Algebra i Logika, Vol. 44, No. 1, pp. 70–80, January–February, 2005.