Properties of subgroups not containing their centralizers

Lemnouar Noui

Displaying similar documents to “Properties of subgroups not containing their centralizers”

On groups satisfying $| G^{'} {| > [G : Z (G)]}^{1 / 2}$ .

Kaplan, Gil, Lev, Arieh (2006)

Beiträge zur Algebra und Geometrie

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Sylow 2-subgroups of solvable Q-groups.

Mohammad Reza Darafsheh, H. Sharifi (2007)

Extracta Mathematicae

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A finite group whose irreducible characters are rational valued is called a rational or a Q-group. In this paper we obtain various results concerning the structure of a Sylow 2-subgroup of a solvable Q-group.

Representation of finite abelian group elements by subsequence sums

David J. Grynkiewicz, Luz E. Marchan, Oscar Ordaz (2009)

Journal de Théorie des Nombres de Bordeaux

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Let $G ≅ C_{n_{1}} \oplus ... \oplus C_{n_{r}}$ be a finite and nontrivial abelian group with $n_{1} | n_{2} | ... | n_{r}$ . A conjecture of Hamidoune says that if $W = w_{1} \cdot ... \cdot w_{n}$ is a sequence of integers, all but at most one relatively prime to $| G |$ , and $S$ is a sequence over $G$ with $| S | \geq | W | + | G | - 1 \geq | G | + 1$ , the maximum multiplicity of $S$ at most $| W |$ , and $σ (W) \equiv 0 mod | G |$ , then there exists a nontrivial subgroup $H$ such that every element $g \in H$ can be represented as a weighted subsequence sum of the form $g = \underset{i = 1}{\sum^{n}} w_{i} s_{i}$ , with $s_{1} \cdot ... \cdot s_{n}$ a subsequence of $S$ . We give two examples showing this does not hold in general, and characterize the...

A new characterization of Mathieu groups

Changguo Shao, Qinhui Jiang (2010)

Archivum Mathematicum

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Let $G$ be a finite group and $nse (G)$ the set of numbers of elements with the same order in $G$ . In this paper, we prove that a finite group $G$ is isomorphic to $M$ , where $M$ is one of the Mathieu groups, if and only if the following hold: (1) $| G | = | M |$ , (2) $nse (G) = nse (M)$ .

Characterizations of groups generated by Kronecker sets

András Biró (2007)

Journal de Théorie des Nombres de Bordeaux

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In recent years, starting with the paper [B-D-S], we have investigated the possibility of characterizing countable subgroups of the torus $T = R / Z$ by subsets of $Z$ . Here we consider new types of subgroups: let $K \subseteq T$ be a Kronecker set (a compact set on which every continuous function $f : K \to T$ can be uniformly approximated by characters of $T$ ), and $G$ the group generated by $K$ . We prove (Theorem 1) that $G$ can be characterized by a subset of $Z^{2}$ (instead of a subset of $Z$ ). If $K$ is finite, Theorem 1 implies our...

Displaying similar documents to “Properties of subgroups not containing their centralizers”

On groups satisfying | G ' | > [ G : Z ( G ) ] 1 / 2 .

Sylow 2-subgroups of solvable Q-groups.

Representation of finite abelian group elements by subsequence sums

A new characterization of Mathieu groups

Characterizations of groups generated by Kronecker sets

On groups satisfying $| G^{'} {| > [G : Z (G)]}^{1 / 2}$ .