Let G = {3a6b10c
Chapter 9, Problem 35E(choose chapter or problem)
Let \(G=\left\{3^{a} 6^{b} 10^{c} \mid a, b, c \in Z\right\}\) under multiplication and \(H=\left\{3^{a} 6^{b} 12^{c} \mid a, b, c \in Z\right\}\) under multiplication. Prove that \(G = \langle 3\rangle \times\langle 6\rangle \times\langle 10\rangle\), whereas \(H \neq\langle 3\rangle \times\langle 6\rangle \times\langle 12\rangle\).
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