cmi-entrance 2019 Q1

cmi-entrance · India · pgmath 4 marks Groups Group Order and Structure Theorems
For a field $F$, $F^{\times}$ denotes the multiplicative group ($F \backslash \{0\}, \times$). Choose the correct statement(s) from below:
(A) Every finite subgroup of $\mathbb{R}^{\times}$ is cyclic;
(B) The order of every non-trivial finite subgroup of $\mathbb{R}^{\times}$ is a prime number;
(C) There are infinitely many non-isomorphic non-trivial finite subgroups of $\mathbb{R}^{\times}$;
(D) The order of every non-trivial finite subgroup of $\mathbb{C}^{\times}$ is a prime number.
For a field $F$, $F^{\times}$ denotes the multiplicative group ($F \backslash \{0\}, \times$). Choose the correct statement(s) from below:\\
(A) Every finite subgroup of $\mathbb{R}^{\times}$ is cyclic;\\
(B) The order of every non-trivial finite subgroup of $\mathbb{R}^{\times}$ is a prime number;\\
(C) There are infinitely many non-isomorphic non-trivial finite subgroups of $\mathbb{R}^{\times}$;\\
(D) The order of every non-trivial finite subgroup of $\mathbb{C}^{\times}$ is a prime number.