Endomorphisms of nilpotent groups of finite rank

2018/01/18 by Hector Durham, Durham, Hector
Engineering · Mathematics · #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings, Modules, and Algebras #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1801.06162

openalex publication_date 2018/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain sufficient criteria for endomorphisms of torsion-free nilpotent groups of finite rank to be automorphisms, by considering the induced maps on the torsion-free abelianisation and the centre. Whilst these results are known in the finitely generated case removing this assumption introduces several difficulties.

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