On D. I. Moldavanskij's question on -separable subgroups of a free group.
On decomposability of finite groups
Let be a finite group. A normal subgroup of is a union of several -conjugacy classes, and it is called -decomposable in if it is a union of distinct -conjugacy classes. In this paper, we first classify finite non-perfect groups satisfying the condition that the numbers of conjugacy classes contained in its non-trivial normal subgroups are two consecutive positive integers, and we later prove that there is no non-perfect group such that the numbers of conjugacy classes contained in its...
On deficient products in infinite groups
On disjoint covering of groups by their cosets
On Dye's condition in nilpotent groups of class 2
On embedding properties of -groups.
On Engel-like congruences
On Equivalence of Finite Group Extensions.
On exact power margin groups
On exponential growth rates for free groups.
Let Fp be a free group of rank p ≥ 2. It is well-known that, with respect to a p-element generating set, that is, a basis, the exponential growth rate of Fp is 2p-1. We show that the exponential growth rate τ of a group G with respect to a p-element generating set X is 2p-1 if and only if G is free on X; otherwise τ < 2p-1. We also prove that, for any finite generating set X of Fp which is disjoint from X-1, the exponential growth rate τ of Fp with respect to X is 2p-1 if and only if X is...
On extensions of an elementary abelian group of order by
On extensions of homomorphisms.
On factor coverings of groups
On finite homomorphic images of the multiplicative group of a division algebra.
On Finite Intersections of "Henselian Valued" Fields.
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 Frobenius groups containing an element of order 3.