Some of the things I've learned every day since Oct 10, 2016
106: Group Isomorphisms
February 1, 2017Posted 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 .