Meaning of automorphism group | Babel Free

Definitions

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

Examples

“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.”

“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.”

“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.”

CEFR level