1- https://doi.org/10.1080/00927870802502837
Polynomial Automorphisms of Soluble Groups
- Oct 9, 2009
- Communications in Algebra
- Gérard Endimioni
Abstract
A polynomial automorphism of a group G is an automorphism of the form . When G is polycyclic, we prove that the set PAut(G) of all polynomial automorphisms forms a polycyclic subgroup of the automorphism group Aut(G). When G is soluble, PAut(G) is not necessarily a subgroup, but we show that the subgroup generated by PAut(G) is soluble. We also give the general form of an element of PAut(G) when G is a torsion-free non-abelian metabelian nilpotent group.
- # Polynomial Automorphisms
- # Automorphism Group
- # Torsion-free Nilpotent Group
- # Non-abelian Nilpotent
- # Torsion-free Nilpotent
- # Metabelian Group
- # Torsion-free Group
- # Non-abelian Group
- # Automorphism Group Aut
- # Polycyclic Subgroup
