hw18 - = G/J H/K . [ Suggestion: Use the rst isomorphism...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Modern Algebra 1 Homework 8.2 Spring 2010 Due March 24 Exercise 5. Let G be a group. Show that if H and K are both normal subgroups of G and H K = { e } then xy = yx for all x H and y K . [ Hint: Consider the element xyx - 1 y - 1 .] Exercise 6. Let G and H be groups and let J G and K H . a. Prove that J × K G × H . b. If J C G and K C H then J × K C G × H and ( G × H ) / ( J × K )
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: = G/J H/K . [ Suggestion: Use the rst isomorphism theorem.] c. Is every subgroup of G H of the form J K ? Exercise 7. If m and n are not relatively prime show that Z m Z n is not cyclic. Exercise 8. Lang, II.4.29....
View Full Document

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.

Ask a homework question - tutors are online