On centrally nilpotent loops
Using a lemma on subnormal subgroups, the problem of nilpotency of multiplication groups and inner permutation groups of centrally nilpotent loops is discussed.
On certain characterizations of barely transitive groups
On certain closed subgroups of .
On cohomological periodicity for infinite groups.
On commuting elemts of groups acting on trees
On computing quaternion quotient graphs for function fields
Let be a maximal -order in a division quaternion algebra over which is split at the place . The present article gives an algorithm to compute a fundamental domain for the action of the group of units on the Bruhat-Tits tree associated to . This action is a function field analog of the action of a co-compact Fuchsian group on the upper half plane. The algorithm also yields an explicit presentation of the group in terms of generators and relations. Moreover we determine an upper bound...
On congruence permutable -sets
An algebraic structure is said to be congruence permutable if its arbitrary congruences and satisfy the equation , where denotes the usual composition of binary relations. To an arbitrary -set satisfying , we assign a semigroup on the base set containing a zero element , and examine the connection between the congruence permutability of the -set and the semigroup .
On connectedness of graphs on direct product of Weyl groups
In this paper, we have studied the connectedness of the graphs on the direct product of the Weyl groups. We have shown that the number of the connected components of the graph on the direct product of the Weyl groups is equal to the product of the numbers of the connected components of the graphs on the factors of the direct product. In particular, we show that the graph on the direct product of the Weyl groups is connected iff the graph on each factor of the direct product is connected.
On cross semigroup varieties and related questions.
On cyclic subgroups of the group .
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...