the definition of an isomorphism is quite natural. An isomorphism of groups may equivalently be defined as an invertible group homomorphism (the inverse...

mathematics, specifically abstract algebra, the isomorphism theorems (also known as Noether's isomorphism theorems) are theorems that describe the relationship...

Babai, László (January 9, 2017), Graph isomorphism update Sun, Xiaorui (2023). "Faster Isomorphism for p-Groups of Class 2 and Exponent p". arXiv:2303...

science Can the graph isomorphism problem be solved in polynomial time? More unsolved problems in computer science The graph isomorphism problem is the computational...

an isomorphism from a structure to itself. An isomorphism between two structures is a canonical isomorphism (a canonical map that is an isomorphism) if...

of order theory, an order isomorphism is a special kind of monotone function that constitutes a suitable notion of isomorphism for partially ordered sets...

abelian groups, then the set of isomorphism classes of extensions of Q {\displaystyle Q} by a given (abelian) group N {\displaystyle N} is in fact a group, which...

topological groups is continuous if and only if it is continuous at some point. An isomorphism of topological groups is a group isomorphism that is also...

an origin induces an isomorphism between the Euclidean space and its associated Euclidean vector space. There is a natural group homomorphism p from E(n)...

mathematics contains the finite groups of small order up to group isomorphism. For n = 1, 2, … the number of nonisomorphic groups of order n is 1, 1, 1, 2,...

logarithm is a group isomorphism of this group to the additive group of real numbers, R {\displaystyle \mathbb {R} } . The multiplicative group of a field F {\displaystyle...

{\displaystyle \eta _{X}} is an isomorphism in D {\displaystyle D} , then η {\displaystyle \eta } is said to be a natural isomorphism (or sometimes natural equivalence...

Isomorphism problem may refer to: graph isomorphism problem group isomorphism problem isomorphism problem of Coxeter groups This disambiguation page lists...

subgroups of G this induces an isomorphism from G to a subgroup of the permutation group of degree [G : H]. In every group G, conjugation is an action of...

is the group isomorphism problem, which asks whether two groups given by different presentations are actually isomorphic. For example, the group with presentation...

{n}}_{d})} as the group isomorphism ⁠ G ≅ ∏ d G d {\displaystyle \textstyle G\cong \prod _{d}G_{d}} ⁠, we have the algebra isomorphism η ∗ : R [ G ] ≅ ⨂...

The isomorphism L2(9) ≅ A6 allows one to see the exotic outer automorphism of A6 in terms of field automorphism and matrix operations. The isomorphism L4(2)...

by S. group automorphism See automorphism. group homomorphism See homomorphism. group isomorphism See isomorphism. homomorphism Given two groups (G, •)...

Look up isomorphism or isomorph in Wiktionary, the free dictionary. Isomorphism or isomorph may refer to: Isomorphism, in mathematics, logic, philosophy...

automorphism groups and topologically invariant in the group isomorphism sense. There is a natural group action of the homeomorphism group of a space on...

{1}}+b\,{\hat {i}}+c\,{\hat {j}}+d\,{\hat {k}}} This map is in fact a group isomorphism. Additionally, the determinant of the matrix is the squared norm of...

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...

group SO+(1, 3). Furthermore, since the kernel of the action (1) is the subgroup {±I}, then passing to the quotient group gives the group isomorphism...

Automorphism group Factor group Fundamental theorem on homomorphisms Group homomorphism Group isomorphism Homomorphism Isomorphism theorem Inner automorphism...

permutation groups) if there exists a bijective map λ : X → Y and a group isomorphism ψ : G → H such that λ(f1(g, x)) = f2(ψ(g), λ(x)) for all g in G and...

generators and relations, because the first isomorphism theorem for ⁠ ϕ {\displaystyle \phi } ⁠ yields an isomorphism ⁠ ⟨ r , f ∣ r 4 = f 2 = ( r ⋅ f ) 2 =...

of logarithms is the story of a correspondence (in modern terms, a group isomorphism) between multiplication on the positive real numbers and addition...

(Serre) the Pontrjagin isomorphism was the main tool for computing the homotopy groups of spheres. In 1954 the Pontrjagin isomorphism was generalized by René...

\log _{b}a} is also unique, and the discrete logarithm amounts to a group isomorphism log b : H → Z . {\displaystyle \log _{b}\colon H\to \mathbf {Z} .}...

only simple group that is a derivative of a group of Lie type that is not a group of Lie type in any series from exceptional isomorphisms. It is sometimes...