Normalizers and self-normalizing subgroups II

Boris Širola

Displaying similar documents to “Normalizers and self-normalizing subgroups II”

The superfocal subgroup

Marian Deaconescu (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Nel presente lavoro vengono dimostrati teoremi d'esistenza di $p$ -complementi normali nei gruppi finiti.

Finite Groups with Weakly s-Permutably Embedded and Weakly s-Supplemented Subgroups

Changwen Li (2011)

Bulletin of the Polish Academy of Sciences. Mathematics

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Suppose G is a finite group and H is a subgroup of G. H is called weakly s-permutably embedded in G if there are a subnormal subgroup T of G and an s-permutably embedded subgroup $H_{s e}$ of G contained in H such that G = HT and $H \cap T \leq H_{s e}$ ; H is called weakly s-supplemented in G if there is a subgroup T of G such that G = HT and $H \cap T \leq H_{s G}$ , where $H_{s G}$ is the subgroup of H generated by all those subgroups of H which are s-permutable in G. We investigate the influence of the existence of s-permutably embedded and...

The Hughes subgroup

Robert Bryce (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let $G$ be a group and $p$ a prime. The subgroup generated by the elements of order different from $p$ is called the Hughes subgroup for exponent $p$ . Hughes [3] made the following conjecture: if $H_{p} (G)$ is non-trivial, its index in $G$ is at most $p$ . There are many articles that treat this problem. In the present Note we examine those of Strauss and Szekeres [9], which treats the case $p = 3$ and $G$ arbitrary, and that of Hogan and Kappe [2] concerning the case when $G$ is metabelian, and $p$ arbitrary. A common...

A conjugacy theorem for subgroups of $G L_{n}$ containing the group of diagonal matrices

N. A. Vavilov (1987)

Colloquium Mathematicae

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On $S$ -quasinormal and $c$ -normal subgroups of a finite group

Shirong Li, Yangming Li (2008)

Czechoslovak Mathematical Journal

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Let $ℱ$ be a saturated formation containing the class of supersolvable groups and let $G$ be a finite group. The following theorems are presented: (1) $G \in ℱ$ if and only if there is a normal subgroup $H$ such that $G / H \in ℱ$ and every maximal subgroup of all Sylow subgroups of $H$ is either $c$ -normal or $S$ -quasinormally embedded in $G$ . (2) $G \in ℱ$ if and only if there is a normal subgroup $H$ such that $G / H \in ℱ$ and every maximal subgroup of all Sylow subgroups of $F^{*} (H)$ , the generalized Fitting subgroup of $H$ , is either $c$ -normal...

On normal subgroups of compact groups

Nikolay Nikolov, Dan Segal (2014)

Journal of the European Mathematical Society

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Among compact Hausdorff groups $G$ whose maximal profinite quotient is finitely generated, we characterize those that possess a proper dense normal subgroup. We also prove that the abstract commutator subgroup $[H, G]$ is closed for every closed normal subgroup $H$ of $G$ .

Injectors of fitting classes of $\mathfrak{G}_{1}$ -groups

Federico Menegazzo, Martin L. Newell (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Fitting classes and injectors are discussed in the class of $\mathfrak{G}_{1}$ -groups. A necessary and sufficient condition for the existence of injectors is given; it is also shown that, when this condition holds, the injectors form a unique conjugacy class.

Orbit spaces, Quillen's Theorem A and Minami's formula for compact Lie groups

Assaf Libman (2011)

Fundamenta Mathematicae

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Let G be a compact Lie group. We present a criterion for the orbit spaces of two G-spaces to be homotopy equivalent and use it to obtain a quick proof of Webb’s conjecture for compact Lie groups. We establish two Minami type formulae which present the p-localised spectrum $Σ^{\infty} B G ₊$ as an alternating sum of p-localised spectra $Σ^{\infty} B H ₊$ for subgroups H of G. The subgroups H are calculated from the collections of the non-trivial elementary abelian p-subgroups of G and the non-trivial p-radical subgroups...

The dual group of a dense subgroup

William Wistar Comfort, S. U. Raczkowski, F. Javier Trigos-Arrieta (2004)

Czechoslovak Mathematical Journal

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Throughout this abstract, $G$ is a topological Abelian group and $\hat{G}$ is the space of continuous homomorphisms from $G$ into the circle group $𝕋$ in the compact-open topology. A dense subgroup $D$ of $G$ is said to determine $G$ if the (necessarily continuous) surjective isomorphism $\hat{G} ↠ \hat{D}$ given by $h \mapsto h | D$ is a homeomorphism, and $G$ is determined if each dense subgroup of $G$ determines $G$ . The principal result in this area, obtained independently by L. Außenhofer and M. J. Chasco, is the following: Every metrizable...

Finite groups whose set of numbers of subgroups of possible order has exactly 2 elements

Changguo Shao, Qinhui Jiang (2014)

Czechoslovak Mathematical Journal

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Counting subgroups of finite groups is one of the most important topics in finite group theory. We classify the finite non-nilpotent groups $G$ whose set of numbers of subgroups of possible orders $n (G)$ has exactly two elements. We show that if $G$ is a non-nilpotent group whose set of numbers of subgroups of possible orders has exactly 2 elements, then $G$ has a normal Sylow subgroup of prime order and $G$ is solvable. Moreover, as an application we give a detailed description of non-nilpotent...

Metrization criteria for compact groups in terms of their dense subgroups

Dikran Dikranjan, Dmitri Shakhmatov (2013)

Fundamenta Mathematicae

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According to Comfort, Raczkowski and Trigos-Arrieta, a dense subgroup D of a compact abelian group G determines G if the restriction homomorphism Ĝ → D̂ of the dual groups is a topological isomorphism. We introduce four conditions on D that are necessary for it to determine G and we resolve the following question: If one of these conditions holds for every dense (or $G_{δ}$ -dense) subgroup D of G, must G be metrizable? In particular, we prove (in ZFC) that a compact abelian group determined...