My Math Forum  

Go Back   My Math Forum > College Math Forum > Abstract Algebra

Abstract Algebra Abstract Algebra Math Forum

LinkBack Thread Tools Display Modes
November 18th, 2007, 01:00 PM   #1
Joined: Nov 2007

Posts: 3
Thanks: 0


Let D-sub-4 be the octic group and G'={e',a,b,c} be the Klein 4-group with e' the identify of G', and a^2=b^2=c^c=e'.

Tabulate a homomorphism Φ : D-sub-4 --> G' with the given requirements.

Φ((1)): e'
Φ((14)(23)): c
Φ((13)): a

We can tell easily that c^2=a^2=e' [But does that matter???]

But, I still need to figure out what maps to b.

The elements are:
(1), (1234), (13)(24), (1432), (24), (14)(23), (13), and (12)(34).

Again, we already know which ones map to e', a, and c. The elements that are left are:
(1234), (13)(24), (1432), (24), and (12)(34).
All of the elements squared are going to map to e' except (1234) and (1432).
This means that (13)(24), (24), and (12)(34) can be a, b, or c. But how do I know which is which?

Also, then what do (1234) and (1432) map to?
mathstresser is offline  

  My Math Forum > College Math Forum > Abstract Algebra


Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
ring homomorphisms tiger4 Abstract Algebra 0 April 20th, 2012 09:21 PM
Galois Theory questions: Homomorphisms wattsup Abstract Algebra 0 November 2nd, 2011 04:45 PM
Ring homomorphisms and kernel norway9k Abstract Algebra 2 November 16th, 2010 11:28 PM
True/False about Homomorphisms and Zero Divisors jkong05 Abstract Algebra 1 May 5th, 2009 02:41 AM
commutative diagram, module homomorphisms fermatprime371 Abstract Algebra 0 December 8th, 2008 06:44 PM

Copyright © 2018 My Math Forum. All rights reserved.