homework 17 (due Apr 15)

due date

Thursday, April 15

instructions

Read Chapter 5 of our textbook up to and including Corollary 5.7. Complete the following exercises:

1, 2, 16

some hints

For 16, proceed by contradiction. That is, assume that the number of elements of order 2 is even; if there are any at all (maybe there are none), call them $g_1, g_2, \ldots, g_k$, where $k$ is even. Consider $H=\{e, g_1, \ldots, g_k\}$. How many elements does $H$ have? Why is $H$ a subgroup? What does the corollary to Lagrange's Theorem (Corollary 5.6) tell us about the non-identity elements of $H$?

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