# 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
89 Citations

### Inverse limit slender groups

• Mathematics
• 2021
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

• Mathematics
• 2000
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

• Mathematics
• 2000
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

• Mathematics
Journal of the Australian Mathematical Society
• 2020
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

• Mathematics
• 2014
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

• Mathematics
• 2000
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

• Mathematics
• 1991
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.