Free product decompositions in images of certain free products of groups

JOURNAL OF ALGEBRA

卷:310

Article

Romanovskii, N. S. ; Wilson, John S.

关键词: free products;    relations;    Magnus Freiheitssatz;   

DOI  :  10.1016/j.jalgebra.2006.08.008

来源: Elsevier

【 摘 要 】

Let F be the free product of n groups and let R be a normal subgroup generated (as a normal subgroup) by m elements of F, where m < n. The Main Theorem gives sufficient conditions for families of fewer than n - m subgroups in certain quotients of F/R to generate their free product. This leads to a more direct proof of a result of the first author, that if G is a group having a presentation with n generators and m relators, where m < n, then any generating set for G contains n - m elements that freely generate a free subgroup of G. Another consequence is that an n-generator one-relator group cannot be generated by fewer than n - 1 subgroups each having a non-trivial abelian normal subgroup. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free