Isomorphism of Groups is an equivalence relation - Chapter 9 - Lecture 2
Автор: Dr. Mrs. Samina S. Boxwala Kale
Загружено: 2021-01-03
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In this video we prove that isomorphism is an equivalence relation on the collection of all groups. We begin by proving that every group is isomorphic to itself. For this we prove that the identity function from a group G to itself is an isomorphism. Hence isomorphism is a reflexive relation. We then prove that this relation is also symmetric as well as transitive.
Link for proof of identity function being a homomorphism:
• Homomorphism: Definition and Examples - Ch...
Link for proof of composition of homomorphisms is a homomorphism:
• Composition of Homomorphisms and Homomorph...
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Link to the previous lecture
• Isomorphism of Groups: Definition & Exampl...
Link to the next lecture
• Essence of Isomorphism of Groups - Chapter...
Link to the first lecture of this chapter
• Isomorphism of Groups: Definition & Exampl...
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