Pure subgroups

Ladislav Bican

Displaying similar documents to “Pure subgroups”

Large free subgroups of automorphism groups of ultrahomogeneous spaces

Szymon Głąb, Filip Strobin (2015)

Colloquium Mathematicae

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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...

Connected transversals -- the Zassenhaus case

Tomáš Kepka, Petr Němec (2000)

Commentationes Mathematicae Universitatis Carolinae

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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 $G$ .

Ulm-Kaplansky invariants of S(KG)/G

P. V. Danchev (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

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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 TI-subgroups and QTI-subgroups of finite groups

Ruifang Chen, Xianhe Zhao (2020)

Czechoslovak Mathematical Journal

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Let $G$ be a group. A subgroup $H$ of $G$ is called a TI-subgroup if $H \cap H^{g} = 1$ or $H$ for every $g \in G$ and $H$ is called a QTI-subgroup if $C_{G} (x) \leq N_{G} (H)$ for any $1 \neq x \in H$ . In this paper, a finite group in which every nonabelian maximal is a TI-subgroup (QTI-subgroup) is characterized.

Torsion points in families of Drinfeld modules

Dragos Ghioca, Liang-Chung Hsia (2013)

Acta Arithmetica

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Let $Φ^{λ}$ be an algebraic family of Drinfeld modules defined over a field K of characteristic p, and let a,b ∈ K[λ]. Assume that neither a(λ) nor b(λ) is a torsion point for $Φ^{λ}$ for all λ. If there exist infinitely many λ ∈ K̅ such that both a(λ) and b(λ) are torsion points for $Φ^{λ}$ , then we show that for each λ ∈ K̅, a(λ) is torsion for $Φ^{λ}$ if and only if b(λ) is torsion for $Φ^{λ}$ . In the case a,b ∈ K, we prove in addition that a and b must be $̅_{p}$ -linearly dependent.

A characterization of Ext(G,ℤ) assuming (V = L)

Saharon Shelah, Lutz Strüngmann (2007)

Fundamenta Mathematicae

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We complete the characterization of Ext(G,ℤ) for any torsion-free abelian group G assuming Gödel’s axiom of constructibility plus there is no weakly compact cardinal. In particular, we prove in (V = L) that, for a singular cardinal ν of uncountable cofinality which is less than the first weakly compact cardinal and for every sequence $(ν_{p} : p \in Π)$ of cardinals satisfying $ν_{p} \leq 2^{ν}$ (where Π is the set of all primes), there is a torsion-free abelian group G of size ν such that $ν_{p}$ equals the p-rank of Ext(G,ℤ)...

Finite groups with some SS-supplemented subgroups

Mengling Jiang, Jianjun Liu (2021)

Czechoslovak Mathematical Journal

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A subgroup $H$ of a finite group $G$ is said to be SS-supplemented in $G$ if there exists a subgroup $K$ of $G$ such that $G = H K$ and $H \cap K$ is S-quasinormal in $K$ . We analyze how certain properties of SS-supplemented subgroups influence the structure of finite groups. Our results improve and generalize several recent results.