Group Theory, lecture 1.5: Orders, subgroups, isomorphism

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We discuss orders of elements, subgroups and isomorphisms of groups.
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You made the explanation really easy to follow, I just have a tiny complain/observation . . .
The way you wrote Z/2Z in the video, doesn't it make it look like a Quotient Group? Isn't the Set of elements of mod 2 supposed to be identified with the notation 2Z?

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I'm curious, is there any method to count the number of groups of order n?

Dr.Cassio_Esteves