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Displaying 61 – 80 of 318

Cyclic and dihedral constructions of even order

Aleš Drápal (2003)

Commentationes Mathematicae Universitatis Carolinae

Let $G (\circ)$ and $G (*)$ be two groups of finite order $n$ , and suppose that they share a normal subgroup $S$ such that $u \circ v = u * v$ if $u \in S$ or $v \in S$ . Cases when $G / S$ is cyclic or dihedral and when $u \circ v \neq u * v$ for exactly $n^{2} / 4$ pairs $(u, v) \in G \times G$ 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 $G (*)$ from a given $G = G (\circ)$ . The constructions, denoted by $G [α, h]$ and $G [β, γ, h]$ , respectively, depend on a coset $α$ (or two cosets $β$ and $γ$ ) modulo $S$ , and on an...

$D_{p} (3)$ (p ≥ 5) can be characterized by its order components

Huaguo Shi, Zhangjia Han, Guiyun Chen (2012)

Colloquium Mathematicae

Let G be a finite group, and $M = D_{p} (3)$ (p ≥ 3). It is proved that G ≅ M if G and M have the same order components.

Defektschranken gewisser Subnormalteiler.

Hermann Heineken (1986)

Mathematische Zeitschrift

Degree problems of representation theory over arbitrary fields of characteristic 0. On theorems of N. Ito and J. G: Thompson.

Bertram Huppert, Roderick Gow (1987)

Journal für die reine und angewandte Mathematik

Degree problems of representation theory over arbitrary fields of characteristic 0. Part 2: Groups which have only two reduces degrees.

Bertram Huppert, Roderick Gow (1988)

Journal für die reine und angewandte Mathematik

Derival automorphisms of groups and a classification problem.

Chiş, Mihai, Chiş, Codruţa (2002)

Novi Sad Journal of Mathematics

Determination of all rigid groups of order not exceeding 60

Panagiotis Soules (1989)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

Distinguishing numbers for graphs and groups.

Tymoczko, Julianna (2004)

The Electronic Journal of Combinatorics [electronic only]

Eine Bemerkung zu den zyklischen Gruppen.

H. Bergmann (1990)

Elemente der Mathematik

Elementary Abelian operator groups.

Pavel Shumyatskiy (1994)

Manuscripta mathematica

Equations in simple matrix groups: algebra, geometry, arithmetic, dynamics

Tatiana Bandman, Shelly Garion, Boris Kunyavskiĭ (2014)

Open Mathematics

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.

Warren Dicks (1994)

Inventiones mathematicae

Estimation of the order of a group generated by a twisted subset.

Belyaev, V.V., Myl'nikov, A.L. (2008)

Sibirskij Matematicheskij Zhurnal

Exact covering systems for groups

M. Parmenter (1984)

Fundamenta Mathematicae

Extreme elements of finite $p$ -groups

Avinoam Mann (1990)

Rendiconti del Seminario Matematico della Università di Padova

Factoring Abelian groups of order $p^{4}$ .

Szabó, Sándor, Amin, Khalid (1996)

Mathematica Pannonica

Factoring an odd abelian group by lacunary cyclic subsets

Sándor Szabó (2010)

Discussiones Mathematicae - General Algebra and Applications

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.

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