# Group isomorphism

A **group isomorphism** is a **isomorphic**. Isomorphic groups have the same properties and the same structure of their

Let (*G*, *) and (*H*, #) be two groups, where "*" and "#" are the binary operations in *G* and *H*, respectively. A *group isomorphism* from (*G*, *) to (*H*, #) is a bijection from *G* to *H*, *i*.*e*. a bijective mapping *f* : *G* → *H* such that for all *u* and *v* in *G* one has

*f* (*u* * *v*) = *f* (*u*) # *f* (*v*).

Two groups (*G*, *) and (*H*, #) are isomorphic if an isomorphism between them exists. This is written:

*G*, *) (*H*, #)

If *H* = *G* and the binary operations # and *