Two groups and are said to be isomorphic if there is a group isomorphism .
Next we name a few necessary conditions for two groups to be isomorphic (with isomorphism as above).
If one group is cyclic, the other one must be cyclic too. Suppose is cyclic generated by an element . Then it is easy to see that is generated by the element . Also if is finitely generated, then is finitely generated as well.
If one group is abelian, the other one must be abelian as well. Indeed, suppose is abelian. Then
and using the injectivity of we conclude .
|Date of creation||2013-03-22 14:01:58|
|Last modified on||2013-03-22 14:01:58|
|Last modified by||alozano (2414)|