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...

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...

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,...

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

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)...

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

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...

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...

{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 ] ≅ ⨂...

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

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)...

{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...

{\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...

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

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...

h_{1}h_{2}\end{aligned}}} is a topological isomorphism, meaning that it is a homeomorphism and a group isomorphism. More generally, G {\displaystyle G} is...

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

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

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...

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

collectively to achieve it List of small groups, a list of finite groups of small order up to group isomorphism Small group learning, an educational approach...

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...

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

circle. This gives the circle group the structure of a one-parameter group, an instance of a Lie group. In fact, up to isomorphism, it is the unique 1-dimensional...

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

The isomorphism can be described as follows: given a group representation ρ : G → GL(V), where V is a vector space over k, GL(V) is the group of its...