Subgroups defining automorphisms in locally nilpotent groups
Copyright policy )Subgroups defining automorphisms in locally nilpotent groups
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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Automorphisms of infinite groups, automorphisms, endomorphisms, hypercentral groups, Generalizations of solvable and nilpotent groups, FOS: Mathematics, 20F28, 20F19, Automorphism groups of groups, locally nilpotent groups, Group Theory (math.GR), Mathematics - Group Theory
Automorphisms of infinite groups, automorphisms, endomorphisms, hypercentral groups, Generalizations of solvable and nilpotent groups, FOS: Mathematics, 20F28, 20F19, Automorphism groups of groups, locally nilpotent groups, Group Theory (math.GR), Mathematics - Group Theory
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