cmi-entrance 2020 Q1

cmi-entrance · India · pgmath 4 marks Groups True/False with Justification

Let $G$ be a group and $N$ be a proper normal subgroup. Pick the true statement(s) from below.
(A) If $N$ and the quotient $G / N$ is finite, then $G$ is finite.
(B) If the complement $G \backslash N$ of $N$ in $G$ is finite, then $G$ is finite.
(C) If both $N$ and the quotient $G / N$ are cyclic, then $G$ is cyclic.
(D) $G$ is isomorphic to $N \times G / N$.

Let $G$ be a group and $N$ be a proper normal subgroup. Pick the true statement(s) from below.\\
(A) If $N$ and the quotient $G / N$ is finite, then $G$ is finite.\\
(B) If the complement $G \backslash N$ of $N$ in $G$ is finite, then $G$ is finite.\\
(C) If both $N$ and the quotient $G / N$ are cyclic, then $G$ is cyclic.\\
(D) $G$ is isomorphic to $N \times G / N$.

Paper Questions

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