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Further Maths : Groups

SS__

What does it mean if two groups are isomorphic?
What does homomorphism mean?

Thanks, Guys!

Reply 1

vc94

Original post by SS__

What does it mean if two groups are isomorphic?
What does homomorphism mean?

Thanks, Guys!

Isomorphism: There is a bijective mapping which is a homomorphism. In effect, the group elements are relabelled.
Homomorphism: A mapping which preserves the structure between group elements.

Just thinking out aloud, obviously there are details to fill in!

Reply 2

SS__

Original post by vc94

Thanks for that, really helpful! Do you happen to know how to find proper subgroups from a group?

The question I'm looking at is M = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, list all the proper subgroups. Please help?