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Displaying 161 – 180 of 220

On the conjugate type vector and the structure of a normal subgroup

Ruifang Chen, Lujun Guo (2022)

Czechoslovak Mathematical Journal

Let $N$ be a normal subgroup of a group $G$ . The structure of $N$ is given when the $G$ -conjugacy class sizes of $N$ is a set of a special kind. In fact, we give the structure of a normal subgroup $N$ under the assumption that the set of $G$ -conjugacy class sizes of $N$ is $(p_{1 n_{1}}^{a_{1 n_{1}}}, \dots, p_{11}^{a_{11}}, 1) \times \dots \times (p_{r n_{r}}^{a_{r n_{r}}}, \dots, p_{r 1}^{a_{r 1}}, 1)$ , where $r > 1$ , $n_{i} > 1$ and $p_{i j}$ are distinct primes for $i \in {1, 2, \dots, r}$ , $j \in {1, 2, \dots, n_{i}}$ .

On the cyclic subgroup separability of free products of two groups with amalgamated subgroup.

Sokolov, E. (2002)

Lobachevskii Journal of Mathematics

On the diameter of the intersection graph of a finite simple group

Xuanlong Ma (2016)

Czechoslovak Mathematical Journal

Let $G$ be a finite group. The intersection graph $Δ_{G}$ of $G$ is an undirected graph without loops and multiple edges defined as follows: the vertex set is the set of all proper nontrivial subgroups of $G$ , and two distinct vertices $X$ and $Y$ are adjacent if $X \cap Y \neq 1$ , where $1$ denotes the trivial subgroup of order $1$ . A question was posed by Shen (2010) whether the diameters of intersection graphs of finite non-abelian simple groups have an upper bound. We answer the question and show that the diameters of intersection...

On the dynamics and the fixed subgroup of a free group automorphism.

Marshall M. Cohen (1989)

Inventiones mathematicae

On the Embedding of Semigroups into Nilpotent Groups

Joseph E. Kuczkowski (1975)

Matematický časopis

On the existence of $f$ -local subgroups in a group.

Sozutov, A.I., Yanchenko, M.V. (2006)

Sibirskij Matematicheskij Zhurnal

On the existence of group localizations under large-cardinal axioms.

Carles Casacuberta, Dirk Scevenels (2001)

RACSAM

Uno de los problemas abiertos más antiguos de la teoría de grupos categórica es si todo par ortogonal (formado por una clase de grupos y una clase de homomorfismos que se determinan mutuamente por ortogonalidad en el sentido de Freyd-Kelly), se halla asociado a un funtor de localización. Se sabe que esto es cierto si se acepta la validez de un cierto axioma de cardinales grandes (el principio de Vopenka), pero no se conoce ninguna demostración mediante los axiomas ordinarios (ZFC) de la teoría de...

On the existence of universal covering spaces for metric spaces and subsets of the Euclidean plane

G. R. Conner, J. W. Lamoreaux (2005)

Fundamenta Mathematicae

We prove several results concerning the existence of universal covering spaces for separable metric spaces. To begin, we define several homotopy-theoretic conditions which we then prove are equivalent to the existence of a universal covering space. We use these equivalences to prove that every connected, locally path connected separable metric space whose fundamental group is a free group admits a universal covering space. As an application of these results, we prove the main result of this article,...

On the existence of universal rational structures for groups.

Grigorenko, O.V., Roman'kov, V.A. (2007)

Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]

On the exponent of the product of two groups

Avinoam Mann (2006)

Rendiconti del Seminario Matematico della Università di Padova

On the Fitting length of $H_{n} (G)$

Gülin Ercan, İsmail Ş. Güloğlu (1993)

Rendiconti del Seminario Matematico della Università di Padova

On the Fixed-Point Set and Commutator Subgroup of an Automorphism of a Group of Finite Rank

B. A. F. Wehrfritz (2012)

Rendiconti del Seminario Matematico della Università di Padova

On the Genus of a Nilpotent Group with Finite Commutator Subgroup.

Guido Mislin, Peter Hilton (1976)

Mathematische Zeitschrift

On the group of automorphisms of finite wreath products

Francesco Fumagalli (2006)

Rendiconti del Seminario Matematico della Università di Padova

On the Group of Norm 1 Elements in a Division Algebra.

M.S. Raghunathan (1987/1988)

Mathematische Annalen

On the group of reduced identities of relatively free solvable groups.

Timoshenko, E.I. (2002)

Sibirskij Matematicheskij Zhurnal

On the Homology Theory of Central Group Extensions II. The Exact Sequence in the General Case

Beno Eckmann, Urs Stammbach, Peter J. Hilton (1972)

Commentarii mathematici Helvetici

On the Homomorphisms of the Integral Linear Groups.

Alexander J. Hahn (1972)

Mathematische Annalen

On the intersection graph of a finite group

Hossein Shahsavari, Behrooz Khosravi (2017)

Czechoslovak Mathematical Journal

For a finite group $G$ , the intersection graph of $G$ which is denoted by $Γ (G)$ is an undirected graph such that its vertices are all nontrivial proper subgroups of $G$ and two distinct vertices $H$ and $K$ are adjacent when $H \cap K \neq 1$ . In this paper we classify all finite groups whose intersection graphs are regular. Also, we find some results on the intersection graphs of simple groups and finally we study the structure of $Aut (Γ (G))$ .

On the intersection of finitely generated subgroups of free groups.

W. S. Jassim (1996)

Revista Matemática de la Universidad Complutense de Madrid

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