hw14 - H : K ]. [ Note: This equality is also true if G is...

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Modern Algebra 1 Homework 6.3 Spring 2010 Due February 24 Exercise 6. Let G be a group and H G . What can you say about H if [ G : H ] = 1? What about if G is finite and [ G : H ] = | G | ? Exercise 7. Use Lagrange’s Theorem to prove that the index is multiplicative in towers . That is, if G is a finite group and K H G then [ G : K ] = [ G : H ][
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Unformatted text preview: H : K ]. [ Note: This equality is also true if G is innite and the subgroups are of nite index, but you dont have to prove that.] Exercise 8. Let G be a nite group and H G . Prove that if [ G : H ] is prime then H is maximal (c.f. Homework 3.3)....
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This note was uploaded on 02/29/2012 for the course MATH 3362 taught by Professor Ryandaileda during the Spring '10 term at Trinity University.

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