Results 51 to 60 of about 2,701,761 (237)

The Hilton–Milnor theorem in higher topoi

Bulletin of the London Mathematical Society, EarlyView.
Abstract In this note, we show that the classical theorem of Hilton–Milnor on finite wedges of suspension spaces remains valid in an arbitrary ∞$\infty$‐topos. Our result relies on a version of James' splitting proved in [Devalapurkar and Haine, Doc. Math.
Samuel Lavenir
wiley   +1 more source

ADDITIVE GROUPS OF ASSOCIATIVE RINGS

Научный вестник МГТУ ГА, 2016
An abelian group is said to be semisimple if it is an additive group of at least one semisimple associative ring. It is proved that the description problem for semisimple groups is reduced to the case of reduced groups. As a consequence, it is shown that
E. I. Kompantseva
doaj  

SSGP topologies on abelian groups of positive finite divisible rank [PDF]

Fundamenta Mathematicae, 244 (2019), 125--145, 2017
Let G be an abelian group. For a subset A of G, Cyc(A) denotes the set of all elements x of G such that the cyclic subgroup generated by x is contained in A, and G is said to have the small subgroup generating property (abbreviated to SSGP) if the smallest subgroup of G generated by Cyc(U) is dense in G for every neighbourhood U of zero of G.
arxiv   +1 more source

Ranks for Families of Theories of Abelian Groups

The Bulletin of Irkutsk State University. Series Mathematics, 2019
The rank for families of theories is similar to Morley rank and can be considered as a measure for complexity or richness of these families. Increasing the rank by extensions of families we produce more rich families and obtaining families with the infinite rank that can be considered as “rich enough”.
Sergey V. Sudoplatov, In. I. Pavlyuk
openaire   +3 more sources

Discrete subgroups of normed spaces are free

Bulletin of the London Mathematical Society, EarlyView.
Abstract Ancel, Dobrowolski and Grabowski (Studia Math. 109 (1994): 277–290) proved that every countable discrete subgroup of the additive group of a normed space is free Abelian, hence isomorphic to the direct sum of a certain number of copies of the additive group of the integers.
Tomasz Kania, Ziemowit Kostana
wiley   +1 more source

Khovanskii's theorem and effective results on sumset structure

Discrete Analysis, 2021
Khovanskii's theorem and effective results on sumset structure, Discrete Analysis 2021:27, 25 pp. Let $A$ be a subset of an Abelian group. The $n$-_fold sumset_ $nA$ of $A$ is the set $\{a_1+\dots+a_n:a_1,\dots,a_n\in A\}$.
Michael J. Curran, Leo Goldmakher
doaj   +1 more source

The birational geometry of GIT quotients

Bulletin of the London Mathematical Society, EarlyView.
Abstract Geometric invariant theory (GIT) produces quotients of algebraic varieties by reductive groups. If the variety is projective, this quotient depends on a choice of polarisation; by work of Dolgachev–Hu and Thaddeus, it is known that two quotients of the same variety using different polarisations are related by birational transformations.
Ruadhaí Dervan, Rémi Reboulet
wiley   +1 more source

The Cotypeset of a Torsion Free Abelian Group of Rank Two [PDF]

Proceedings of the American Mathematical Society, 1982
The cotypeset (set of types of rank one factors) of a torsion free abelian group of rank two is characterized.
W. J. Wickless, C. Vinsonhaler
openaire   +2 more sources

Spectra of subrings of cohomology generated by characteristic classes for fusion systems

Bulletin of the London Mathematical Society, EarlyView.
Abstract If F$\mathcal {F}$ is a saturated fusion system on a finite p$p$‐group S$S$, we define the Chern subring Ch(F)${\operatorname{Ch}}(\mathcal {F})$ of F$\mathcal {F}$ to be the subring of H∗(S;Fp)$H^*(S;{\mathbb {F}}_p)$ generated by Chern classes of F$\mathcal {F}$‐stable representations of S$S$. We show that Ch(F)${\operatorname{Ch}}(\mathcal {
Ian J. Leary, Jason Semeraro
wiley   +1 more source

On the Root-class Residuality of HNN-extensions of Groups

Моделирование и анализ информационных систем, 2014
Let K be an arbitrary root class of groups. This means that K contains at least one non-unit group, is closed under taking subgroups and direct products of a finite number of factors and satisfies the Gruenberg condition: if 1 ≤ Z ≤ Y ≤ X is a subnormal ...
E. A. Tumanova
doaj   +1 more source