Malnormality and centers in one-relator relative presentations

2012/12/20 by Denis E. Lurye, Denis Lurye, Lurye, Denis
Mathematics · #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.1212.5173

23 pages, 17 figures. arXiv admin note: substantial text overlap with arXiv:1010.4220

openalex publication_date 2012/12/20 · arxiv created 2012/12/23 · arxiv updated 2012/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let H be a group obtained from a group G by adding one generator and one relator which is a proper power of a unimodular word. The main aim of this paper is to prove that G is a malnormal subgroup of H. This implies that if G is a nontrivial group, then the group H has a trivial center.

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