hw29 - ψ ◦ ϕ G → K is an isomorphism c Show that the...

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

View Full Document Right Arrow Icon
Intro to Abstract Math Homework 29 Fall 2009 Due December 4 Exercise 84. Show that Q and R (under addition) are not cyclic. [ Suggestion: Argue by contradiction. If a were a generator, what would need to be true about a/ 2?] Exercise 85. Let G , H and K be groups. a. Show that if ϕ : G H is an isomorphism, then ϕ - 1 : H G is an isomorphism. b. Show that if ϕ : G H and ψ : H K are isomorphisms, then
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ψ ◦ ϕ : G → K is an isomorphism. c. Show that the notion of isomorphism is an equivalence relation on the collection of all groups. Exercise 86. Show that no two of Z 8 , U (16) and D 4 are isomorphic. Remember, the operation in Z 8 is addition mod 8, and the operation in U (16) is multiplication mod 16....
View Full Document

This note was uploaded on 02/29/2012 for the course MATH 3326 taught by Professor Ryandaileda during the Fall '09 term at Trinity University.

Ask a homework question - tutors are online