# Today I Learned

Some of the things I've learned every day since Oct 10, 2016

## 106: Group Isomorphisms

February 1, 2017

Posted by on In group theory, a **group ****isomorphism **between 2 groups does not simply refer to an ‘isomorphism’ between the underlying sets of , but to a special type of homomorphism between them: one which is bijective. In a sense, isomorphic groups are the same group, just with different symbols representing their elements and operations — something which is not necessarily true if they’re homomorphic or if just their underlying sets are isomorphic.

In particular, if is a group isomorphism, then

- is abelian is abelian
- for all .

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