The Root-Class Residuality of the Fundamental Groups of Graphs of Groups

Siberian Mathematical Journal - Consider a class  $ \mathcal{C} $ of groups containing at least one nontrivial group and closed under subgroups, extensions, and Cartesian...     

On the Root-Class Residuality of Certain Free Products of Groups with Normal Amalgamated Subgroups

Russian Mathematics - Let $${\cal K}$$ be a root class of groups closed under taking quotient groups, G be a free product of groups A and B with amalgamated subgroups H and K. Let also H be normal...     

On Intersections of Certain Nilpotent Subgroups in Finite Groups

Mathematical Notes - It is proved that, in any finite group $$G$$ with nilpotent subgroups $$A$$ and $$B$$ and the condition $$Acap B^gunlhdlangle A,B^grangle$$ for any $$g$$ in $$G$$ ,...     

The Automorphic Conjugacy Problem for Subgroups of Fundamental Groups of Compact Surfaces

Let be a compact connected surface with basepoint x and H ₁ and H ₂ be two finitely generated subgroups of ₁(, x) on finite sets of generators. It is proved that there exists an algorithm which decides whether there is an automorphism for which (H ₁) = H ₂, and if so, it finds such.     

局部环上正交群中一类子群的扩群

定出了局部环上正交群中一类子群的扩群,得到了如下结果:设R是局部环,M是R的唯一极大理想,O(2m,R)为R上正交群.对R的任意理想S,G(2m,S)表示子群{A BC D∈O(2m,R)|B∈Sm×m}.如果char(R)≠2,m≥3,G(2m,0)≤X≤G(2m,M),那么存在R的理想S,使得X=G(2m,S).     

On Certain Distributive Lattices of Subgroups of Finite Soluble Groups

In this paper, we prove the following result. Let ξ be a saturated formation and ∑ a Hall system of a soluble group G. Let X be a w-solid set of maximal subgroups of G such that ∑ reduces into each element of X. Consider in G the following three subgroups： the ξ-normalizer D of G associated with ∑; the X-prefrattini subgroup W = W（G, X） of G; and a hypercentrally embedded subgroup T of G. Then the lattice ζ（T, W, D） generated by T, D and W is a distributive lattice of pairwise permutable subgroups of G with the cover and avoidance property. This result remains true for the lattice ,ζ（V, W, D）, where V is a subgroup of G whose Sylow subgroups are also Sylow subgroups of hypercentrally embedded subgroups of G such that ∑ reduces into V.     

The Root Class Residuality of the Tree Product of Groups with Amalgamated Retracts

Siberian Mathematical Journal - Given a root class $mathscr{K}$ of groups, we prove that the tree product of residually $mathscr{K}$ -groups with amalgamated retracts is a residually...     

Subgroup Separability and Linearity of Certain Graphs of Groups

We show that if the fundamental group of a finite graph of groups with finitely generated Abelian vertex groups is subgroup separable, then it is linear.     

Fundamental Groups of Graphs of Cyclic Subgroup Separable and Weakly Potent Groups

We give a characterization of the cyclic subgroup separability and weak potency of the fundamental group of a graph of polycyclic-by-finite groups and free-by-finite groups amalgamating edge subgroups of the form × D,where h has infinite order and D is finite.     

On the Equality of Certain Subgroups of the Automorphism Groups of Finite p-Groups

Mathematical Notes - Let G be a finite non-Abelian p-group, where p is a prime. An automorphism α of G is called an IA-automorphism if x?1α(x) ∈ G′ for all x ∈ G....     

Nilpotent Subgroups of Groups with All Subgroups Subnormal

It is proved that in groups with all subgroups subnormal everynilpotent subgroup is contained in a normal nilpotent subgroup.     

Matchings Including or Excluding Certain Edge Sets in Bipartite Graphs

Necessary and sufficient conditions are obtained for a bipartitegraph to admit a matching which includes a preassigned set ofedges and excludes another preassigned set of edges. 1991 MathematicsSubject Classification 05C70.     

Groups with Few Nonmodular Subgroups

Let G be a Tarski-free group such that the join of all nonmodular subgroups of G is a proper subgroup in G. It is proved that G contains a finite normal subgroup N such that the quotient group G/N has a modular subgroup lattice.__________Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 10, pp. 1419 – 1423, October, 2004.     

Groups with Polycyclic Non-Normal Subgroups

The structure of groups in which many subgroups have a certain property X has been investigated for several choices of the property X. Groups whose non-normal subgroups satisfy certain finite rank conditions are studied in this article. In particular, a classification of groups in which every subgroup is either normal or polycyclic is given.(Dedicated to Mario Curzio on the occasion of his 70th birthday)1991 Mathematics Subject Classification: 20F16     

Groups with All Subgroups Pronormal-by-Finite

A subgroup X of a group G is called pronormal-by-finite if there exists a pronormal subgroup Y of G such that Y ≤ X and |X : Y| is finite. The structure of (generalized) soluble groups in which all subgroups are pronormal-by-finite is investigated. Among other results, it is proved in particular that a finitely generated soluble group with such property is central-by-finite, provided that it has no infinite dihedral sections.     

Soluble Groups with Few Non-Baer Subgroups

We characterize non-finitely generated soluble groups with the maximal condition on non-Baer subgroups and prove that a non-Baer soluble group is a ^ˇCernikov group or it has an infinite properly descending series of non-Baer subgroups.