Exercise 3.2.1 (First application of Lagrange's Theorem)

Question

Which of the following are permissible orders for subgroups of order $120$: $1,\, 2,\ 5,\, 9,\, 15,\, 60, \, 240$? For each permissible order give the corresponding index.

Richard Ganaye · Accepted Answer

\begin{proof} 
By Lagrange's Theorem, the cardinal of a subgroup $H$ of $G$ must divide $|G| = 120$, so the permissible orders for subgroups $H$ among $1,\, 2,\ 5,\, 9,\, 15,\, 60, \, 240$ are $1,\, 2,\,5,\, 15,\, 60$, whose respective indices $(G:H)$ are $120,\, 60,\, 24,\, 8,\, 2.$

\end{proof}

Exercise 3.2.1 (First application of Lagrange's Theorem)

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Exercise 3.2.1 (First application of Lagrange's Theorem)

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