Explain why a group of order 4m where m is odd must have a
Chapter 24, Problem 65E(choose chapter or problem)
Explain why a group of order 4m where m is odd must have a subgroup isomorphic to \(Z_4\) or \(Z_2 \oplus Z_2\) but cannot have both a subgroup isomorphic to \(Z_4\) and a subgroup isomorphic to \(Z_2 \oplus Z_2\). Show that S4 has a subgroup isomorphic to \(Z_4\) and a subgroup isomorphic to \(Z_2 \oplus Z_2\).
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