Let us consider G , H . There exists h which is an isomorphism. Let us note that the predicate G and H are isomorphic is reflexive. If h is a monomorphism, then G and Im h are isomorphic. For all strict groups G , H such that G is trivial and H is trivial holds G and H are isomorphic.
H are isomorphic.
G and G are isomorphic. Let G , H be strict groups and h be a homomorphism from G to H . Let G , H be strict groups. Then G is finite and H is finite. For all strict groups G , H such that G and H are isomorphic and G is trivial holds H is trivial.