cmi-entrance 2022 Q1

cmi-entrance · India · pgmath 4 marks Groups Group Order and Structure Theorems

By a simple group, we mean a group $G$ in which the only normal subgroups are $\left\{ 1 _ { G } \right\}$ and $G$. Pick the correct statement(s) from below.
(A) No group of order 625 is simple.
(B) $\mathrm { GL } ( 2 , \mathbb { R } )$ is simple.
(C) Let $G$ be a simple group of order 60. Then $G$ has exactly six subgroups of order 5 .
(D) Let $G$ be a group of order 60. Then $G$ has exactly seven subgroups of order 3 .

By a simple group, we mean a group $G$ in which the only normal subgroups are $\left\{ 1 _ { G } \right\}$ and $G$. Pick the correct statement(s) from below.\\
(A) No group of order 625 is simple.\\
(B) $\mathrm { GL } ( 2 , \mathbb { R } )$ is simple.\\
(C) Let $G$ be a simple group of order 60. Then $G$ has exactly six subgroups of order 5 .\\
(D) Let $G$ be a group of order 60. Then $G$ has exactly seven subgroups of order 3 .

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