automorphism group

plural automorphism groups

1. group theoryThe 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.

   4 more examples

   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.

   1984, José M. Isidro, László L. Stachó, Holomorphic Automorphism Groups in Banach Spaces: An Elementary Introduction, Elsevier (North-Holland), page vi

   Recently Droste, Holland and Macpherson in [DHM1], [DHM2] and [DHM3] investigated various questions concerning the automorphism groups of homogeneous #92;aleph#95;0-categorical trees.

   1993, Matatyahu Rubin, The Reconstruction of Trees from Their Automorphism Groups, American Mathematical Society, page 5

   Unlike the classical integration theory, the non-commutative theory comes with the intrinsic dynamics of the modular automorphism group. This chapter is devoted to the elementary theory of the modular automorphism groups.

   2002, Masamichi Takesaki, Theory of Operator Algebras II, Springer, page 91

   Synonyms: symmetry group, symmetric group