Abstract Algebra. Properties of Isomorphisms

Title: Abstract Albegra. Properties of Isomorphisms

Abstract: Whenever two groups are isomorphic, essentially all of the properties that you can think of about these groups are shared. We describe some of these properties that are shared between isomorphic groups. We also show how this gives you tools for proving two groups are not isomorphic.

[hyperduality]

Injective is dual to surjective synthesizes bijective or isomorphism.
Thesis (invertible homomorphisms, isomorphism) is dual to anti-thesis (non invertible homomorphisms) creates the converging thesis or synthesis -- the time independent Hegelian dialectic.
Absolute sameness (isomorphism) is dual to relative sameness (homomorphism).
Same is dual to different, waves (same state, Bosons) are dual to particles (different states, Fermions) -- Quantum duality.
Invertible is dual to non invertible.
Duality creates reality.
"Always two there are" -- Yoda.