On a conjecture of M. E. Watkins on graphical regular representations of finite groups
On a constant of Turán and Erdös
On a hierarchy of groups of computable automorphisms.
On a Theorem of Livingstone and Wagner.
On automorphism groups of boolean algebras
On automorphism groups of planar lattices
The structure of automorphisms of planar lattices is analyzed.
On automorphisms of algebras with a single unary operation
On automorphisms of Weyl algebra
On B-injectors of symmetric groups Sₙ and alternating groups Aₙ: a new approach
The aim of this paper is to introduce the notion of BG-injectors of finite groups and invoke this notion to determine the B-injectors of Sₙ and Aₙ and to prove that they are conjugate. This paper provides a new, more straightforward and constructive proof of a result of Bialostocki which determines the B-injectors of the symmetric and alternating groups.
On certain characterizations of barely transitive groups
On Certain Classes of rigid groups
On Certain Maximal Subgroups of Symmetric or Alternating Groups.
On chirality groups and regular coverings of regular oriented hypermaps
We prove that if the Walsh bipartite map of a regular oriented hypermap is also orientably regular then both and have the same chirality group, the covering core of (the smallest regular map covering ) is the Walsh bipartite map of the covering core of and the closure cover of (the greatest regular map covered by ) is the Walsh bipartite map of the closure cover of . We apply these results to the family of toroidal chiral hypermaps induced by the family of toroidal bipartite maps...
On classifying subsets of natural numbers by their computable permutations.
On degrees of three algebraic numbers with zero sum or unit product
Let α, β and γ be algebraic numbers of respective degrees a, b and c over ℚ such that α + β + γ = 0. We prove that there exist algebraic numbers α₁, β₁ and γ₁ of the same respective degrees a, b and c over ℚ such that α₁ β₁ γ₁ = 1. This proves a previously formulated conjecture. We also investigate the problem of describing the set of triplets (a,b,c) ∈ ℕ³ for which there exist finite field extensions K/k and L/k (of a fixed field k) of degrees a and b, respectively, such that the degree of the...
On double coverings of some rotary hypermaps.
On finite loops whose inner mapping groups have small orders
We investigate the situation that the inner mapping group of a loop is of order which is a product of two small prime numbers and we show that then the loop is soluble.
On Graphical Regular Representations of Direct Products of Groups.
On Groups with Several Doubly-Transitive Permuation Representations.
On imprimitive groups with small degree