Solvable groups of finite non-abelian sectional rank

We study non-Abelian solvable groups of finite non-Abelian sectional rank and prove that their (special) rank is finite.     

Locally nilpotent groups of finite non-Abelian sectional rank

We introduce the notion of non-Abelian sectional rank of a group and study locally nilpotent non-Abelian groups of finite non-Abelian sectional rank. It is proved that the (special) rank of these groups is finite.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 4, pp. 452–455, April, 1995.     

Locally almost solvable groups of finite non-Abelian rank

It is proved that a nonperiodic, locally almost solvable group of finite non-Abelian 0-rank has finite (special) rank.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 4, pp. 477–482, April, 1990.     

Groups of finite non-Abelian sectional rank

We study non-Abelian locally finite groups and non-Abelian locally solvable groups of finite non-Abelian sectional rank and prove that their (special) rank is finite. Dnepropetrovsk University, Dnepropetrovsk. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 10, pp. 1324–1331, October, 1997.     

Solvable subgroups of finite simple groups

This article is the author's abstract of his dissertation for the degree Doctor of Physico-mathematical Sciences. The dissertation was defended on September 17, 1973, at the session of the Academic Council on the conferring of academic degrees in the mathematical sciences of the Uralian Order of the Red Banner of Labor of the A. M. Gor'kii State University. The official opponents were: Professor A. I. Shirshov, Corresponding Member of the Academy of Sciences of the USSR and Doctor of Physicomathematical Sciences; Professor A. I. Kostrikin, Doctor of Physicomathematical Sciences; Professor A. I. Starostin, Doctor of Physicomathematical Sciences; Professor L. A. Shemetkov, Doctor of Physico-mathematical Sciences. The chief institution was the Institute of Mathematics, Academy of Sciences of the Ukrainian SSR.Translated from Matematicheskie Zametki, Vol. 16, No. 5, pp. 833–842, November, 1974.     

Solvable line-transitive automorphism groups of finite linear spaces

Let S be a finite linear space, and letG be a group of automorphisms of S. IfG is soluble and line-transitive, then for a givenk but a finite number of pairs of (S, G),S hasv= p ⁿ points andG ⩽AΓL(1,p ⁿ ).     

On residually finite groups of finite general rank

Following A. I.Mal’tsev, we say that a group G has finite general rank if there is a positive integer r such that every finite set of elements of G is contained in some r-generated subgroup. Several known theorems concerning finitely generated residually finite groups are generalized here to the case of residually finite groups of finite general rank. For example, it is proved that the families of all finite homomorphic images of a residually finite group of finite general rank and of the quotient of the group by a nonidentity normal subgroup are different. Special cases of this result are a similar result of Moldavanskii on finitely generated residually finite groups and the following assertion: every residually finite group of finite general rank is Hopfian. This assertion generalizes a similarMal’tsev result on the Hopf property of every finitely generated residually finite group.     

Hypercentral groups of finite subnormal rank

We introduce the notion of subnormal rank of a group and study hypercentral groups of finite subnormal rank. We construct an example of a hypercentral group that has a finite subnormal rank and infinite (special) rank.Translated from Ukrainskii Matematicheskii Zhurnal, Vol.47, No. 11, pp. 1577–1580, November, 1995.     

Approximability of finite rank soluble groups by certain classes of finite groups

For soluble groups of finite rank we obtain the necessary and sufficient condition to be a virtually residually finite p-group. We also prove that a soluble group G of finite rank is residually π-finite for some finite set π of primes if and only if it has no subgroups of type Q and the torsion radical of G is a finite group.