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 ∞ . 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 ∞ can be extended to a large free subgroup of S ∞ , and, under Martin’s Axiom, any free subgroup of S ∞ of cardinality less than can also be extended to a large free subgroup of S ∞ . 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 ∩ H u ∩ H v = 1 whenever u , v ∈ G ∖ H and u v - 1 ∈ 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 ∪ 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 ∩ H g = 1 or H for every g ∈ G and H is called a QTI-subgroup if C G ( x ) ≤ N G ( H ) for any 1 ≠ x ∈ 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 ∈ Π ) of cardinals satisfying ν p ≤ 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 ∩ 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.

A characterization of the linear groups L 2 ( p )

Alireza Khalili Asboei, Ali Iranmanesh (2014)

Czechoslovak Mathematical Journal

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Let G be a finite group and π e ( G ) be the set of element orders of G . Let k ∈ π e ( G ) and m k be the number of elements of order k in G . Set nse ( G ) : = { m k : k ∈ π e ( G ) } . In fact nse ( G ) is the set of sizes of elements with the same order in G . In this paper, by nse ( G ) and order, we give a new characterization of finite projective special linear groups L 2 ( p ) over a field with p elements, where p is prime. We prove the following theorem: If G is a group such that | G | = | L 2 ( p ) | and nse ( G ) consists of 1 , p 2 - 1 , p ( p + ϵ ) / 2 and some numbers divisible by 2 p , where p is a prime...