automorphism group

Definitions

1. 1

   The group of automorphisms of a given set or other mathematical object, with the group…

   The group of automorphisms of a given set or other mathematical object, with the group operation being function composition.

   • The automorphism group of a set is the set's symmetric group.
   • The automorphism group of a finite-dimensional vector space (respectively, projective space) is the space's general linear group (respectively, projective linear group).
   • Moreover, we think that this approach to the automorphism groups of Banach space domains may also serve as motivating and illustrative material in introducing students to the theory of Lie groups and complex manifolds.

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