A conjugacy theorem for subgroups of $GL_n$ containing the group of diagonal matrices

N. A. Vavilov

Displaying similar documents to “A conjugacy theorem for subgroups of $G L_{n}$ containing the group of diagonal matrices”

The superfocal subgroup

Marian Deaconescu (1984)

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

Similarity:

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

Ulm-Kaplansky invariants of S(KG)/G

P. V. Danchev (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

Let G be an infinite abelian p-group and let K be a field of the first kind with respect to p of characteristic different from p such that $s_{p} (K) = ℕ$ or $s_{p} (K) = ℕ \cup 0$ . The main result of the paper is the computation of the Ulm-Kaplansky functions of the factor group S(KG)/G of the normalized Sylow p-subgroup S(KG) in the group ring KG modulo G. We also characterize the basic subgroups of S(KG)/G by proving that they are isomorphic to S(KB)/B, where B is a basic subgroup of G.

On normal subgroups of compact groups

Nikolay Nikolov, Dan Segal (2014)

Journal of the European Mathematical Society

Similarity:

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 $G$ .

Nested matrices and inverse $M$ -matrices

Jeffrey L. Stuart (2015)

Czechoslovak Mathematical Journal

Similarity:

Given a sequence of real or complex numbers, we construct a sequence of nested, symmetric matrices. We determine the $L U$ - and $Q R$ -factorizations, the determinant and the principal minors for such a matrix. When the sequence is real, positive and strictly increasing, the matrices are strictly positive, inverse $M$ -matrices with symmetric, irreducible, tridiagonal inverses.

The superfocal subgroup

Marian Deaconescu (1984)

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

Similarity:

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

On the matrix negative Pell equation

Aleksander Grytczuk, Izabela Kurzydło (2009)

Discussiones Mathematicae - General Algebra and Applications

Similarity:

Let N be a set of natural numbers and Z be a set of integers. Let M₂(Z) denotes the set of all 2x2 matrices with integer entries. We give necessary and suficient conditions for solvability of the matrix negative Pell equation (P) X² - dY² = -I with d ∈ N for nonsingular X,Y belonging to M₂(Z) and his generalization (Pn) $\sum_{i = 1}^{n} X ₂_{i} - d \sum_{i = 1}^{n} Y ²_{i} = - I$ with d ∈ N for nonsingular $X_{i}, Y_{i} \in M ₂ (Z)$ , i=1,...,n.

Large free subgroups of automorphism groups of ultrahomogeneous spaces

Szymon Głąb, Filip Strobin (2015)

Colloquium Mathematicae

Similarity:

We consider the following notion of largeness for subgroups of $S_{\infty}$ . A group G is large if it contains a free subgroup on generators. We give a necessary condition for a countable structure A to have a large group Aut(A) of automorphisms. It turns out that any countable free subgroup of $S_{\infty}$ can be extended to a large free subgroup of $S_{\infty}$ , and, under Martin’s Axiom, any free subgroup of $S_{\infty}$ of cardinality less than can also be extended to a large free subgroup of $S_{\infty}$ . Finally, if Gₙ are countable...

On closed subgroups of the group of homeomorphisms of a manifold

Frédéric Le Roux (2014)

Journal de l’École polytechnique — Mathématiques

Similarity:

Let $M$ be a triangulable compact manifold. We prove that, among closed subgroups of ${Homeo}_{0} (M)$ (the identity component of the group of homeomorphisms of $M$ ), the subgroup consisting of volume preserving elements is maximal.

On quotients of the space of orderings of the field ℚ(x)

Paweł Gładki, Bill Jacob (2016)

Banach Center Publications

Similarity:

In this paper we present a method of obtaining new examples of spaces of orderings by considering quotient structures of the space of orderings $(X_{ℚ (x)}, G_{ℚ (x)})$ - it is, in general, nontrivial to determine whether, for a subgroup $G ₀ \subset G_{ℚ (x)}$ the derived quotient structure $(X_{ℚ (x)} |_{G ₀}, G ₀)$ is a space of orderings, and we provide some insights into this problem. In particular, we show that if a quotient structure arising from a subgroup of index 2 is a space of orderings, then it necessarily is a profinite one.

On $R$ -conjugate-permutability of Sylow subgroups

Xianhe Zhao, Ruifang Chen (2016)

Czechoslovak Mathematical Journal

Similarity:

A subgroup $H$ of a finite group $G$ is said to be conjugate-permutable if $H H^{g} = H^{g} H$ for all $g \in G$ . More generaly, if we limit the element $g$ to a subgroup $R$ of $G$ , then we say that the subgroup $H$ is $R$ -conjugate-permutable. By means of the $R$ -conjugate-permutable subgroups, we investigate the relationship between the nilpotence of $G$ and the $R$ -conjugate-permutability of the Sylow subgroups of $A$ and $B$ under the condition that $G = A B$ , where $A$ and $B$ are subgroups of $G$ . Some results known in the literature are improved...

Expansion and random walks in ${SL}_{d} (ℤ / p^{n} ℤ)$ : I

Jean Bourgain, Alex Gamburd (2008)

Journal of the European Mathematical Society

Similarity:

We prove that the Cayley graphs of ${SL}_{d} (ℤ / p^{n} ℤ)$ are expanders with respect to the projection of any fixed elements in ${SL}_{d} (ℤ)$ generating a Zariski dense subgroup.

A computation of positive one-peak posets that are Tits-sincere

Marcin Gąsiorek, Daniel Simson (2012)

Colloquium Mathematicae

Similarity:

A complete list of positive Tits-sincere one-peak posets is provided by applying combinatorial algorithms and computer calculations using Maple and Python. The problem whether any square integer matrix $A \in ₙ (ℤ)$ is ℤ-congruent to its transpose $A^{t r}$ is also discussed. An affirmative answer is given for the incidence matrices $C_{I}$ and the Tits matrices $C ̂_{I}$ of positive one-peak posets I.

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

Changwen Li (2011)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

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...

Connected transversals -- the Zassenhaus case

Tomáš Kepka, Petr Němec (2000)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

In this short note, it is shown that if $A, B$ are $H$ -connected transversals for a finite subgroup $H$ of an infinite group $G$ such that the index of $H$ in $G$ is at least 3 and $H \cap H^{u} \cap H^{v} = 1$ whenever $u, v \in G ∖ H$ and $u v^{- 1} \in G ∖ H$ then $A = B$ is a normal abelian subgroup of $G$ .

G-matrices, $J$ -orthogonal matrices, and their sign patterns

Frank J. Hall, Miroslav Rozložník (2016)

Czechoslovak Mathematical Journal

Similarity:

A real matrix $A$ is a G-matrix if $A$ is nonsingular and there exist nonsingular diagonal matrices $D_{1}$ and $D_{2}$ such that $A^{- T} = D_{1} A D_{2}$ , where $A^{- T}$ denotes the transpose of the inverse of $A$ . Denote by $J = diag (\pm 1)$ a diagonal (signature) matrix, each of whose diagonal entries is $+ 1$ or $- 1$ . A nonsingular real matrix $Q$ is called $J$ -orthogonal if $Q^{T} J Q = J$ . Many connections are established between these matrices. In particular, a matrix $A$ is a G-matrix if and only if $A$ is diagonally (with positive diagonals) equivalent to a column permutation...

Displaying similar documents to “A conjugacy theorem for subgroups of G L n containing the group of diagonal matrices”

Displaying similar documents to “A conjugacy theorem for subgroups of $G L_{n}$ containing the group of diagonal matrices”