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.
Subgroups defining automorphisms in locally nilpotent groups / Cutolo, Giovanni; C., Nicotera. - In: FORUM MATHEMATICUM. - ISSN 0933-7741. - STAMPA. - 15:4(2003), pp. 489-506. [10.1515/form.2003.027]
Subgroups defining automorphisms in locally nilpotent groups
CUTOLO, GIOVANNI;
2003
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.File in questo prodotto:
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