Counting -groups and nilpotent groups
Cyclic and dihedral constructions of even order
Let and be two groups of finite order , and suppose that they share a normal subgroup such that if or . Cases when is cyclic or dihedral and when for exactly pairs have been shown to be of crucial importance when studying pairs of 2-groups with the latter property. In such cases one can describe two general constructions how to get all possible from a given . The constructions, denoted by and , respectively, depend on a coset (or two cosets and ) modulo , and on an...
(p ≥ 5) can be characterized by its order components
Let G be a finite group, and (p ≥ 3). It is proved that G ≅ M if G and M have the same order components.
Defektschranken gewisser Subnormalteiler.
Degree problems of representation theory over arbitrary fields of characteristic 0. On theorems of N. Ito and J. G: Thompson.
Degree problems of representation theory over arbitrary fields of characteristic 0. Part 2: Groups which have only two reduces degrees.
Derival automorphisms of groups and a classification problem.
Determination of all rigid groups of order not exceeding 60
Distinguishing numbers for graphs and groups.
Eine Bemerkung zu den zyklischen Gruppen.
Elementary Abelian operator groups.
Equations in simple matrix groups: algebra, geometry, arithmetic, dynamics
We present a survey of results on word equations in simple groups, as well as their analogues and generalizations, which were obtained over the past decade using various methods: group-theoretic and coming from algebraic and arithmetic geometry, number theory, dynamical systems and computer algebra. Our focus is on interrelations of these machineries which led to numerous spectacular achievements, including solutions of several long-standing problems.
Equivalence of the strengthened Hanna Neumann conjecture and the amalgamated graph conjecture.
Estimation of the order of a group generated by a twisted subset.
Exact covering systems for groups
Extreme elements of finite -groups
Factoring Abelian groups of order .
Factoring an odd abelian group by lacunary cyclic subsets
It is a known result that if a finite abelian group of odd order is a direct product of lacunary cyclic subsets, then at least one of the factors must be a subgroup. The paper gives an elementary proof that does not rely on characters.
Factoring by nonsubgroup factors.
Factorization problems in class number two