Free σ-products and noncommutatively slender groups

@article{Eda1992FreeA,
  title={Free $\sigma$-products and noncommutatively slender groups},
  author={Katsuya Eda},
  journal={Journal of Algebra},
  year={1992},
  volume={148},
  pages={243-263}
}
  • K. Eda
  • Published 1 May 1992
  • Mathematics
  • Journal of Algebra

Inverse limit slender groups

Classically, an abelian group G is said to be slender if every homomorphism from the countable product Z to G factors through the projection to some finite product Z. Various authors have proposed

PII: S0166-8641(99)00103-0

In this paper we study the combinatorial structure of the Hawaiian earring group, by showing that it can be represented as a group of transfinite wordson a countably infinite alphabet exactly

The failure of the uncountable non-commutative Specker Phenomenon

Higman proved in 1952 that every free group is non-commutatively slender, this is to say that if G is a free group and h is a homomorphism from the countable complete free product (X_omega Z) to G,

INFINITARY COMMUTATIVITY AND ABELIANIZATION IN FUNDAMENTAL GROUPS

Abstract Infinite product operations are at the forefront of the study of homotopy groups of Peano continua and other locally path-connected spaces. In this paper, we define what it means for a space

Root extraction in one-relator groups and slenderness

ABSTRACT In this note we strengthen a result of Newman and use it to prove a conjecture of Nakamura stated in [10] that torsion-free one-relator groups are noncommutatively slender.

Archipelago groups

The classical archipelago is a non-contractible subset of R3 which is homeomorphic to a disk except at one non-manifold point. Its fundamental group, A , is the quotient of the topologist’s product

On the homology of infinite graphs with ends

The topological cycle space C(G) of an infinite graph G has been introduced in 2004 by Diestel and Kuhn. It enabled them to extend the cycle space theorems, which show the interaction of the cycle

QUESTION AND HOMOMORPHISMS ON ARCHIPELAGO GROUPS

The classical archipelago group is a quotient group of the fundamental group of the Hawaiian earring by the normal closure of the free group of countable rank, which is denoted by A(Z). Since the

The Singular Homology of the Hawaiian Earring

The singular homology groups of compact CW‐complexes are finitely generated, but the groups of compact metric spaces in general are very easy to generate infinitely and our understanding of these

The nonabelian product modulo sum

. It is shown that if { H n } n ∈ ω is a sequence of groups without invo- lutions, with 1 < | H n | ≤ 2 ℵ 0 , then the topologist’s product modulo the finite words is (up to isomorphism) independent
...

References

SHOWING 1-9 OF 9 REFERENCES

The Theory Of Groups

Introduction Normal subgroups and homomorphisms Elementary theory of abelian groups Sylow theorems Permutation groups Automorphisms Free groups Lattices and composition series A theorem of Frobenius

A factor of singular homology

Singular homology is a beautiful theory, in which we can see a clear correspondence between Algebra and Topology. However, it behaves badly on topological spaces which are not locally simply

Additive Gruppen von Folgen Ganzer Zahlen

Die Folgen ganzer Zahlen {a n } (vom Typus ω) bilden auf Grund der Addition {a n } + {b n } = {a n + b n } eine abelsche Gruppe F. Diese Gruppe F und gewisse ihrer Untergruppen sollen im folgenden

Algebraic Topology

The focus of this paper is a proof of the Nielsen-Schreier Theorem, stating that every subgroup of a free group is free, using tools from algebraic topology.