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• # Artykuł - szczegóły

## Open Mathematics

2014 | 12 | 3 | 436-444

## Relation modules of infinite groups, II

EN

### Abstrakty

EN
Let F n denote the free group of rank n and d(G) the minimal number of generators of the finitely generated group G. Suppose that R ↪ F m ↠ G and S ↪ F m ↠ G are presentations of G and let $$\bar R$$ and $$\bar S$$ denote the associated relation modules of G. It is well known that $$\bar R \oplus (\mathbb{Z}G)^{d(G)} \cong \bar S \oplus (\mathbb{Z}G)^{d(G)}$$ even though it is quite possible that . However, to the best of the author’s knowledge no examples have appeared in the literature with the property that . Our purpose here is to exhibit, for each integer k ≥ 1, a group G that has presentations as above such that . Our approach depends on the existence of nonfree stably free modules over certain commutative rings and, in particular, on the existence of certain Hurwitz-Radon systems of matrices with integer entries discovered by Geramita and Pullman. This approach was motivated by results of Adams concerning the number of orthonormal (continuous) vector fields on spheres.

EN

436-444

wydano
2014-03-01
online
2013-12-21

### Twórcy

autor
• The University of Alabama

### Bibliografia

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