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
On locally graded barely transitive groups
We show that a barely transitive group is totally imprimitive if and only if it is locally graded. Moreover, we obtain the description of a barely transitive group G for the case G has a cyclic subgroup 〈x〉 which intersects non-trivially with all subgroups and for the case a point stabilizer H of G has a subgroup H 1 of finite index in H satisfying the identity χ(H 1) = 1, where χ is a multi-linear commutator of weight w.
On locally graded non-periodic barely transitive groups
On Permutation Groups of Degree 2p.
On Permutation Groups of Prime Power Order.
On Prime Ideals in Representation Rings.
On Primitive Permutation Groups Containing a Cycle.
On Projective Planes of Type (5, m).
On -analogs of recursions for the number of involutions and prime order elements in symmetric groups.
On soluble groups of automorphisms of nonorientable Klein surfaces
We classify up to topological type nonorientable bordered Klein surfaces with maximal symmetry and soluble automorphism group provided its solubility degree does not exceed 4. Using this classification we show that a soluble group of automorphisms of a nonorientable Riemann surface of algebraic genus q ≥ 2 has at most 24(q-1) elements and that this bound is sharp for infinitely many values of q.
On some flag-transitive non-classical -geometries. II.
On some Jordan-Hölder-Dedekind type theorems in lattices.
On Subgroups Generated by a Root Triple.
On supersoluble groups acting on Klein surfaces.