-
preserving all of its structure. The set of all
automorphisms of an
object forms a group,
called the
automorphism group. It is,
loosely speaking, the symmetry...
-
adjective "inner".
These inner automorphisms form a
subgroup of the
automorphism group, and the
quotient of the
automorphism group by this
subgroup is defined...
- to itself.
Automorphisms may be
defined in this way both for
directed graphs and for
undirected graphs. The
composition of two
automorphisms is another...
- In mathematics, the
automorphism group of an
object X is the
group consisting of
automorphisms of X
under composition of morphisms. For example, if X is...
- set of
automorphisms of g {\displaystyle {\mathfrak {g}}} are
denoted Aut ( g ) {\displaystyle {\text{Aut}}({\mathfrak {g}})} , the
automorphism group...
-
subgroups are
conjugate by an
inner automorphism, so to
study outer automorphisms it
suffices to
consider automorphisms that fix a
given Borel subgroup....
- subgroup. An IA
automorphism is thus an
automorphism that
sends each
coset of the
commutator subgroup to itself. The IA
automorphisms of a
group form...
-
space that
obeys Kolmogorov's zero–one law. All
Bernoulli automorphisms are K-
automorphisms (one says they have the K-property), but not vice versa. Many...
- mathematics, the
automorphisms and
outer automorphisms of the
symmetric groups and
alternating groups are both
standard examples of
these automorphisms, and objects...
- non-trivial
automorphisms are
outer automorphisms. Non-abelian
groups have a non-trivial
inner automorphism group, and
possibly also
outer automorphisms. Group...
