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Lifting Automorphisms of Quotients by Central Subgroups (1304.4632v1)
Published 16 Apr 2013 in math.GR
Abstract: Given a finitely presented group $G$, we wish to explore the conditions under which automorphisms of quotients $G/N$ can be lifted to automorphisms of $G$. We discover that in the case where $N$ is a central subgroup of $G$, the question of lifting can be reduced to solving a certain matrix equation. We then use the techniques developed to show that $Inn(G)$ is not characteristic in $Aut(G)$, where $G$ is a metacyclic group of order $pn$, $p\neq 2$.