On finite subgroups of groups of type VF.
On free subgroups of generalized triangle groups.
On free subgroups of units in quaternion algebras
It is well known that for the ring H(ℤ) of integral quaternions the unit group U(H(ℤ) is finite. On the other hand, for the rational quaternion algebra H(ℚ), its unit group is infinite and even contains a nontrivial free subgroup. In this note (see Theorem 1.5 and Corollary 2.6) we find all intermediate rings ℤ ⊂ A ⊆ ℚ such that the group of units U(H(A)) of quaternions over A contains a nontrivial free subgroup. In each case we indicate such a subgroup explicitly. We do our best to keep the arguments...
On free subgroups of units in quaternion algebras II
Let A ⊆ ℚ be any subring. We extend our earlier results on unit groups of the standard quaternion algebra H(A) to units of certain rings of generalized quaternions H(A,a,b) = ((-a,-b)/A), where a,b ∈ A. Next we show that there is an algebra embedding of the ring H(A,a,b) into the algebra of standard Cayley numbers over A. Using this embedding we answer a question asked in the first part of this paper.
On genus and embeddings of torsion-free nilpotent groups of class two.
On groups of plolynomial subgroup growth.
On Groups whose Contranormal Subgroups are Normally Complemented
2000 Mathematics Subject Classification: 20F16, 20E15.Groups in which every contranormal subgroup is normally complemented has been considered. The description of such groups G with the condition Max-n and such groups having an abelian nilpotent residual satisfying Min-G have been obtained.
On groups with many nearly maximal subgroups
A subgroup of a group is nearly maximal if the index is infinite but every subgroup of properly containing has finite index, and the group is called nearly if all its subgroups of infinite index are intersections of nearly maximal subgroups. It is proved that an infinite (generalized) soluble group is nearly if and only if it is either cyclic or dihedral.
On homomorphic images of locally graded groups
On hypercentral subgroups of infinite groups
On inert subgroups of a group
On irreducible, infinite, nonaffine Coxeter groups
The following results are proved: The center of any finite index subgroup of an irreducible, infinite, nonaffine Coxeter group is trivial; Any finite index subgroup of an irreducible, infinite, nonaffine Coxeter group cannot be expressed as a product of two nontrivial subgroups. These two theorems imply a unique decomposition theorem for a class of Coxeter groups. We also prove that the orbit of each element other than the identity under the conjugation action in an irreducible, infinite, nonaffine...
On Kurosh-Amitsur radicals of finite groups.
On linearly ordered subgroups of a lattice ordered group
On Locallay Indicable Groups.
On locally graded non-periodic barely transitive groups
On maximal subgroups of minimax groups
It is proved that a soluble residually finite minimax group is finite-by-nilpotent if and only if it has only finitely many maximal subgroups which are not normal.
On maximal subgroups of the general linear group over the field of rational functions.
On mutual commutants of generalized carpet subgroups.
On non-periodic groups whose finitely generated subgroups are either permutable or pronormal
The current article considers some infinite groups whose finitely generated subgroups are either permutable or pronormal. A group is called a generalized radical, if has an ascending series whose factors are locally nilpotent or locally finite. The class of locally generalized radical groups is quite wide. For instance, it includes all locally finite, locally soluble, and almost locally soluble groups. The main result of this paper is the followingTheorem. Let be a locally generalized radical...