Finite graphs of groups with isomorphic fundamental groups

Translated from Algebra i Logika, Vol. 30, No. 5, pp. 595–623, September–October, 1991.     

Finite groups of outer automorphisms of free groups

Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 32, No. 5, pp. 82–100, September–October, 1991.     

Infinite generation of automorphism groups of free pro-p groups

Omsk. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 34, No. 4, pp. 153–159, July–August, 1993.     

Demushkin groups

Let G be a finitely generated pro-p-group with d=d_G>1 generators and a single defining relation. Then, if G is not a Demushkin group, G contains a maximal subgroup with more than p (d–2)+2 generators.Translated from Matematicheskie Zametki, Vol. 14, No. 1, pp. 121–126, July, 1973.     

Abelian-by-FC-hypercentral groups

A splitting theorem for FC-hypercentral group G and zG-module of finite rank is obtained. According to this theorem, under certain conditions, every extension E of the zG-module A by the group G is split and all the complements to A in E are conjugate in E.Published in Ukraninskii Matematicheskii Zhurnal, Vol. 43, Nos. 7 and 8, pp. 1038–1042, July–August, 1991.     

Linear groups

The paper is based on material reviewed in RefZhMat during 1971–1977 and continues a survey of the same name which appeared in this series in 1971. In light of the Tits alternative two old areas have now acquired special importance-free linear groups and solvable linear groups; they are given special attention. Other areas are discussed in somewhat more detail than previously.Translated from Itogi Nauki i Tekhniki, Algebra, Topologiya, Geometriya, Vol. 16, pp. 35–89, 1978.     

Abelian groups

In the present, third survey of reviews of articles on Abelian groups are included papers reviewed during 1972–1978. Here, as in the previous surveys, the questions concerning finite Abelian groups, topological groups, ordered groups, group algebras, modules, structures of subgroups, as well as the questions connected with logic, are not touched on.Translated from Itogi Nauki i Tekhniki, Algebra, Topologiya, Geometriya, Vol. 17, pp. 3–63, 1979.     

Nil radicals in groups

Translated from Algebra i Logika, Vol. 30, No. 1, pp. 102–105, January–February, 1991.     

Verbal products of groups

Translated fromAlgebra i Logika, Vol. 32, No. 2, pp. 160–176, March–April, 1993.     

Embedding theorems for groups with involutions and a characterization of Chernikov groups

Translated from Algebra i Logika, Vol. 27, No. 1, pp. 100–121, January–February, 1988.     

Lattice-ordered groups which are constructed with the aid of totally ordered groups

Translated from Algebra i Logika, Vol. 28, No. 5, pp. 524–533, September–October, 1989.     

Action of primitive groups

Translated from Algebra i Logika, Vol. 28, No. 3, pp. 337–363, May–June, 1989.     

Characterization of layer-finite groups

Translated from Algebra i Logika, Vol. 28, No. 6, pp. 687–704, November–December, 1989.     

Tate cohomologies and Browder-Livesay groups of dihedral groups

Translated from Matematicheskie Zametki, Vol. 54, No. 2, pp. 44–55, August, 1993.     

Brouwer-Livsey groups

Translated from Matematicheskie Zametki, Vol. 51, No. 3, pp. 122–127, March, 1992.     

Socle and socle-finite groups

Four well-known recently posed problems connected with groups that have upper socle series are solved.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, Nos. 7 and 8, pp. 1066–1069, July–August, 1991.     

Factor morphisms of nilpotent groups

Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 32, No. 3, pp. 119–125, May–June, 1991.     

Fully transitive torsion-free Abelian groups

Translated from Algebra i Logika, Vol. 29, No. 5, pp. 549–560, September–October, 1990.     

Imbedding of periodic groups in simple periodic groups

It is proved that each periodic group is isomorphic to a subgroup of some simple periodic group.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 6, pp. 845–847, June, 1992.     

Linear groups

This survey article covers papers abstracted inReferativnyi Zhurnal Matematika during the period 1978–1982 and is a continuation of the surveys Linear groups published in 1967, 1971, and 1977 in the seriesAlgebra, Topology, Geometry (Itogi Nauki i Tekhniki). The main things under consideration are linear groups over rings and the structure of infinite linear groups. Some very recent results are also mentioned.Translated from Itogi Nauki i Tekhniki, Seriya Algebra, Topologiya, Geometriya, Vol. 21, pp. 135–182, 1983.