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

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 ⊕ ... ⊕ 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 · ... · 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 | ≥ | W | + | G | - 1 ≥ | G | + 1 , the maximum multiplicity of S at most | W | , and σ ( W ) ≡ 0 mod | G | , then there exists a nontrivial subgroup H such that every element g ∈ H can be represented as a weighted subsequence sum of the form g = ∑ n i = 1 w i s i , with s 1 · ... · 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 ⊆ T be a Kronecker set (a compact set on which every continuous function f : K → 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...