Abstract
A finite presentation F/N of a group G is called efficient if dF(N) = d(H2(G)) + d(F) – r(H1(G)). A finitely presented group is called efficient if it admits an efficient presentation. We show that a finitely presented group embeds into an efficient group.
Publisher
Cambridge University Press (CUP)
Reference27 articles.
1. Some new efficient soluble groups
2. Efficient presentations for finite simple groups and related groups
3. On Torsion-Free Groups with Infinitely Many Ends
4. 3. Baik Y. G. and Pride S. J. , On the efficiency of Coxeter-groups, preprint, University of Glasgow, 1995.
5. 2. Baik Y. G. and Pride S. J. , Generators of the second homotopy module of presentations arising from group constructions, preprint, Glasgow University, 1993.
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. On defining groups efficiently without using inverses;Mathematical Proceedings of the Cambridge Philosophical Society;2002-07
2. Embeddings into k-Efficient Groups;Journal of Algebra;2001-09
3. The efficiency of standard wreath product;Proceedings of the Edinburgh Mathematical Society;2000-06