Subgroups defining automorphisms in locally nilpotent groups

Details Subgroups defining automorphisms in locally nilpotent groups Subgroups defining automorphisms in locally nilpotent groups

2001-09-21

arxiv.org/abs/math/0109160v1

Mathematics

Group Theory

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

Scientific paper

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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