How to verify if the groups #(RR,+)# and #(CC##,)# are isomorphic?

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Answer 1 · 2017-04-22T08:23:00

See explanation...

Note that #(CC^*, *)# contains a non-identity element that is self inverse, namely:

#(-1)*(-1) = 1#

whereas all non-identity elements in #(RR, +)# are not self inverse:

If #x != 0# then #x+x != 0#

So the two groups cannot be isomorphic.

How to verify if the groups #(RR,+)# and #(CC#*#,*)# are isomorphic?