Subgroups defining automorphisms in locally nilpotent groups

2001/09/21 by Giovanni Cutolo, Cutolo, Giovanni, Chiara Nicotera +1
Mathematics · #20F19 #20F28 #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #math.GR #msc:20F19 #msc:20F28

paper · pdf · doi:10.48550/arxiv.math/0109160

14 pages - no figures - to appear on Forum Mathematicum --- plain TeX requires eplain + additional macros files

arxiv created 2001/09/21 · openalex publication_date 2001/09/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate some situation in which automorphisms of a group G are uniquely determined by their restrictions to a proper subgroup H. Much of the paper is devoted to studying under which additional hypotheses this property forces G to be nilpotent if H is. As an application we prove that certain countably infinite locally nilpotent groups have uncountably many (outer) automorphisms.

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