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1. Automorphism: In mathematics, an automorphism is an isomorphism from a mathematical object to itself. It is, in some sense, a symmetry of the object, and a way of mapping the object to itself while preserving all of its structure. (Isomorphism of an object to itself) [100%] 2024-01-03 [Morphisms] [Abstract algebra]...
2. Automorphism: An isomorphism (isomorphic mapping) of a system of objects onto itself. The totality of all automorphisms of an arbitrary algebraic system forms a group, and the study of this group is an important and powerful tool in the study of ... (Mathematics) [100%] 2023-01-26
3. Automorphism: In algebra, an automorphism of an abstract algebraic structure is an isomorphism of the structure with itself, that is, a permutation of the underlying set which respects all algebraic operations. The automorphisms typically form a group, the automorphism group of ... [100%] 2022-07-01
4. Stokes-Automorphismus: Der Stokes-Automorphismus ist ein Begriff aus der Écalle-Theorie (Theorie der resurgenten Funktionen) und der asymptotischen Analysis. Der Automorphismus stellt einen Zusammenhang zwischen zwei gerichteten Borel-Resummierungen bzw. [71%] 2023-05-15
5. Sastry automorphism: In mathematics, a Sastry automorphism, is an automorphism of a field of characteristic 2 satisfying some rather complicated conditions related to the problem of embedding Ree groups of type F4 into Chevalley groups of type F4. They were introduced by ... [70%] 2023-06-24 [Finite groups] [Finite fields]...
6. Contragredient automorphism: to an automorphism of a right module over a ring The automorphism of the left -module (* denotes taking the dual or adjoint module) that is adjoint to the inverse automorphism to . More generally, if is an automorphism between a right ... (Mathematics) [70%] 2023-10-19
7. Derived automorphism: in ergodic theory A transformation $ T _ {X} $ defined by using an automorphism $ T $ of a measure space $ ( M , \mu ) $ and a measurable subset $ X \subset M $ of positive measure such that almost-all points of $ X $ return to $ X ... (Mathematics) [70%] 2023-10-17
8. Frobenius automorphism: An element of a Galois group of a special type. It plays a fundamental role in class field theory. (Mathematics) [70%] 2023-10-27
9. Regular automorphism: An automorphism $ \phi $ of a group $ G $ such that $ g \phi \neq g $ for every non-identity element $ g $ of $ G $( that is, the image of every non-identity element of a group under a regular automorphism must be different ... (Mathematics) [70%] 2022-12-30
10. Kolmogorov automorphism: In mathematics, a Kolmogorov automorphism, K-automorphism, K-shift or K-system is an invertible, measure-preserving automorphism defined on a standard probability space that obeys Kolmogorov's zero–one law. All Bernoulli automorphisms are K-automorphisms (one says they ... [70%] 2023-09-15 [Ergodic theory]
11. Automorphism group: 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 a finite-dimensional vector space, then the automorphism group of X is the group ... (Mathematical group formed from the automorphisms of an object) [70%] 2024-02-13 [Group automorphisms]
12. Aperiodic automorphism: of a measure space An automorphism $T$ of a measure space such that its periodic points, i.e. the points $x$ for which $T^k(x) = x$ for some $k>0$, form a set of measure zero. (Mathematics) [70%] 2022-10-23
13. Special automorphism: constructed from an automorphism $S$ of a measure space $(X,\nu)$ and a function $f$ (defined on $X$ and taking positive integral values) An automorphism $T$ of a certain new measure space $(M,\mu)$ constructed in the following way. The ... (Mathematics) [70%] 2023-10-25
14. Bernoulli automorphism: An automorphism of a measure space, which describes Bernoulli trials and their generalization — a sequence of independent trials with the same result and with the same probability distribution. Let $ A $ be the collection of all possible outcomes of a trial ... (Mathematics) [70%] 2023-10-12
15. Inner automorphism: In abstract algebra an inner automorphism is an automorphism of a group, ring, or algebra given by the conjugation action of a fixed element, called the conjugating element. They can be realized via simple operations from within the group itself ... (Automorphism of a group, ring, or algebra given by the conjugation action of one of its elements) [70%] 2023-06-12 [Group theory]
16. Field automorphism: In field theory, a field automorphism is an automorphism of the algebraic structure of a field, that is, a bijective function from the field onto itself which respects the fields operations of addition and multiplication. The automorphisms of a given ... [70%] 2023-07-20
17. Class automorphism: In mathematics, in the realm of group theory, a class automorphism is an automorphism of a group that sends each element to within its conjugacy class. The class automorphisms form a subgroup of the automorphism group. [70%] 2023-08-15 [Group theory] [Group automorphisms]...
18. Inner automorphism: of a group $G$ An automorphism $\phi$ such that $$ \phi(x) = g^{-1} x g $$ for a certain fixed element $g \in G$: that is, $\phi$ is conjugation by $g$. The set of all inner automorphisms of $G$ forms a ... (Mathematics) [70%] 2023-10-19
19. Integral automorphism: The same as a special automorphism, constructed from an automorphism $ T $ of a measure space $ ( X , \mu ) $ and a function $ F $( given on this space and taking values in the positive integers). The term "integral automorphism" is mostly used in ... (Mathematics) [70%] 2023-10-17
20. Graph automorphism: An isomorphic mapping of a graph onto itself (cf. Graph isomorphism). (Mathematics) [70%] 2023-07-13 [Graph theory]