cmi-entrance 2013 QA1

cmi-entrance · India · pgmath 4 marks Groups Group Order and Structure Theorems
Pick the correct statement(s) below.
(a) There exists a group of order 44 with a subgroup isomorphic to $\mathbb { Z } / 2 \oplus \mathbb { Z } / 2$.
(b) There exists a group of order 44 with a subgroup isomorphic to $\mathbb { Z } / 4$.
(c) There exists a group of order 44 with a subgroup isomorphic to $\mathbb { Z } / 2 \oplus \mathbb { Z } / 2$ and a subgroup isomorphic to $\mathbb { Z } / 4$.
(d) There exists a group of order 44 without any subgroup isomorphic to $\mathbb { Z } / 2 \oplus \mathbb { Z } / 2$ or to $\mathbb { Z } / 4$.
Pick the correct statement(s) below.\\
(a) There exists a group of order 44 with a subgroup isomorphic to $\mathbb { Z } / 2 \oplus \mathbb { Z } / 2$.\\
(b) There exists a group of order 44 with a subgroup isomorphic to $\mathbb { Z } / 4$.\\
(c) There exists a group of order 44 with a subgroup isomorphic to $\mathbb { Z } / 2 \oplus \mathbb { Z } / 2$ and a subgroup isomorphic to $\mathbb { Z } / 4$.\\
(d) There exists a group of order 44 without any subgroup isomorphic to $\mathbb { Z } / 2 \oplus \mathbb { Z } / 2$ or to $\mathbb { Z } / 4$.