ऑटोमॉर्फिज्म इसके अंग्रेजी अर्थ का उदाहरण

The Stone–von Neumann theorem states that this representation is essentially unique: if \rho' is another such representation, there exists an automorphism.

and the conjugating automorphism is projectively unique, i.

So any automorphism of the Heisenberg group, inducing the identity on the center, acts on this representation \mathcal H—to be precise, the action is only well-defined up to multiplication by a non-zero constant.

The automorphisms of the Heisenberg group (fixing its center) form the symplectic group, so at first sight this seems to give an action of the symplectic group on \mathcal H.

However, the action is only defined up to multiplication by a nonzero constant, in other words, one can only map the automorphism of the group to the class [\psi]\in \operatorname{PU}(\mathcal H).

The group G acts as an automorphism group of the design.

A multiplier of a difference set D in group G is a group automorphism \phi of G such that D^{\phi} gD for some g \in G.

If G is abelian and \phi is the automorphism that maps h \mapsto h^t, then t is called a numerical or Hall multiplier.

It has been conjectured that if p is a prime dividing k-\lambda and not dividing v, then the group automorphism defined by g\mapsto g^p fixes some translate of D (this is equivalent to being a multiplier).

Every 2-design with a regular automorphism group is dev for some difference family B.

Alternatively it is the group of all automorphisms of the algebraic closure of K that fix K.

The absolute Galois group is well-defined up to inner automorphism.

The Frobenius automorphism Fr is a canonical (topological) generator of GK.