Results 81 to 90 of about 228,669 (269)

Structure of quasiconvex virtual joins

Journal of Topology, Volume 18, Issue 2, June 2025.
Abstract Let G$G$ be a relatively hyperbolic group and let Q$Q$ and R$R$ be relatively quasiconvex subgroups. It is known that there are many pairs of finite index subgroups Q′⩽fQ$Q^{\prime } \leqslant _f Q$ and R′⩽fR$R^{\prime } \leqslant _f R$ such that the subgroup join ⟨Q′,R′⟩$\langle Q^{\prime }, R^{\prime } \rangle$ is also relatively quasiconvex,
Lawk Mineh
wiley   +1 more source

Colimits of abelian groups

Journal of Algebra, 2015
In this paper we study the colimit N_2(G) of abelian subgroups of a discrete group G. This group is the fundamental group of a subspace B(2,G) of the classifying space BG. We describe N_2(G) for certain groups, and apply our results to study the homotopy type of the space B(2,G). We give a list of classes of groups for which B(2,G) is not an Eilenberg--
openaire   +3 more sources

Some ugly aleph_1-free abelian groups [PDF]

arXiv, 2001
Given an aleph_1-free abelian group G we characterize the class C_G of all torsion abelian groups T satisfying Ext(G,T)=0 assuming the continuum hypothesis CH. Moreover, in Godel's constructable universe we prove that this characterizes C_G for arbitrary torsion-free abelian G. It follows that there exist some ugly aleph_1-free abelian groups.
arxiv  

From uncountable abelian groups to uncountable nonabelian groups [PDF]

arXiv, 2020
The present note surveys my research related to generalizing notions of abelian group theory to non-commutative case and applying them particularly to investigate fundamental groups.
arxiv  

An Algebraic Roadmap of Particle Theories

Annalen der Physik, Volume 537, Issue 4, April 2025.
The SO(10) grand unified theory, the Georgi–Glashow SU(5) grand unified theory, the Pati–Salam model, the Left–Right Symmetric model, and the Standard model have been studied extensively since the 1970s. Recasting these models in a division algebraic language elucidates how they are each in fact connected.
Nichol Furey
wiley   +1 more source

Canonical Decompositions of Abelian Groups [PDF]

arXiv, 2020
Every torsion--free abelian group of finite rank has two essentially unique complete direct decompositions whose summands come from specific classes of groups.
arxiv  

A characterization of some finite simple groups by their character codegrees

Mathematische Nachrichten, Volume 298, Issue 4, Page 1356-1369, April 2025.
Abstract Let G$G$ be a finite group and let χ$\chi$ be a complex irreducible character of G$G$. The codegree of χ$\chi$ is defined by cod(χ)=|G:ker(χ)|/χ(1)$\textrm {cod}(\chi)=|G:\textrm {ker}(\chi)|/\chi (1)$, where ker(χ)$\textrm {ker}(\chi)$ is the kernel of χ$\chi$.
Hung P. Tong‐Viet
wiley   +1 more source

On diagrams for abelian groups

Journal of Number Theory, 1970
AbstractLet ɒ be the ring of integers of an algebraic number field and p a prime ideal. Then if n is a positive integer, ɒ/pn is a primary ring with prime ideal p̄ = p/pn and the p̄i/p̄i+1 (0 ≤ i < n) are isomorphic groups under addition. Generalizing this idea, the author has defined the primary ring R with prime ideal N to be homogeneous if there is ...
openaire   +2 more sources

Reflexive group topologies on Abelian groups [PDF]

arXiv, 2009
It is proved that any infinite Abelian group of infinite exponent admits a non-discrete reflexive group topology.
arxiv  

Locally constant fibrations and positivity of curvature

Bulletin of the London Mathematical Society, Volume 57, Issue 4, Page 1005-1025, April 2025.
Abstract Up to finite étale cover, any smooth complex projective variety X$X$ with nef anti‐canonical bundle is a holomorphic fibre bundle over a smooth projective variety with trivial canonical class (K‐trivial variety for short) with locally constant transition functions. We show that this result is optimal by proving that any projective fibre bundle
Niklas Müller
wiley   +1 more source