For a field F, F × denotes the multiplicative group (F \ {0}, ×).

Question

For a field F, F
× denotes the multiplicative group (F \ {0}, ×). Prove the correct
statement(s) and find counter examples for incorrect statements from below:

(A) Every finite subgroup of R
× is cyclic;

(B) The order of every non-trivial finite subgroup of R
× is a prime number;

(C) There are infinitely many non-isomorphic non-trivial finite subgroups of R
×;

(D) The order of every non-trivial finite subgroup of C
× is a prime number.

Answer 1

Hint: If $a\in \Bbb C^\times$ generates a finite subgroup, then $|a|=1$.