automorphisms's Usage Examples:

The set of all automorphisms of an object forms a group, called the automorphism group.

These inner automorphisms form a subgroup of the automorphism group, and the quotient of the automorphism.

In mathematics, Hurwitz's automorphisms theorem bounds the order of the group of automorphisms, via orientation-preserving conformal mappings, of a compact.

analysis, Tomita–Takesaki theory is a method for constructing modular automorphisms of von Neumann algebras from the polar decomposition of a certain involution.

The composition of two automorphisms is another.

mathematics, the automorphism group of an object X is the group consisting of automorphisms of X.

the inner automorphisms.

As abstract group there are in addition to these 10 inner and 10 outer automorphisms, 20 more outer automorphisms; e.

precisely 84(g − 1) automorphisms, where g is the genus of the surface.

This number is maximal by virtue of Hurwitz's theorem on automorphisms (Hurwitz 1893).

automorphism group of G and Inn(G) is the subgroup consisting of inner automorphisms.

The composition of two automorphisms is again an automorphism, and with this operation the set of all automorphisms of a group G, denoted by Aut(G).

diagrams also have self-isomorphisms or "automorphisms".

Diagram automorphisms correspond to outer automorphisms of the Lie algebra, meaning that the outer.

The set of all automorphisms is a subset of End(X) with a group structure, called the automorphism.

Most fundamentally, this involves the study of one-parameter automorphisms of the algebra of all bounded operators on the Hilbert space of observables.

These transformation laws are automorphisms of the state space, that is bijective transformations which preserve.

of the fixed points of a set of field automorphisms is a field called the fixed field of the set of automorphisms.

extensions as follows: If E is a given field, and G is a finite group of automorphisms of E with fixed field F, then E/F is a Galois extension.

In every category, the automorphisms of an object always form a group, called the automorphism group of the.

more specifically the study of field automorphisms is an important part of Galois theory.

Just as the automorphisms of an algebraic structure form a group.

These automorphisms do not project to automorphisms of SO(8).