Turn on thread page Beta
    • Thread Starter

    Example. If G = D_8 then the subgroup H = \{e, a, a^2, a^3\} is a normal subgroup, since its index in G is 8/4 = 2. We may see this directly as follows: clearly ghg^(−1) in H for all g, h \in H , so it suffices to consider g \not\in H; then g = ba^i , h = a^j , and

    ghg^{−1} = ba^i(a^j)(ba^i)^(−1) = (ba^i)(a^j)(a^(−i))(b^(−1)) = b(a^j)(b^(−1)) = (bab^(−1))^j = (a^(−1))^j = a^(−j) in H

    Sorry, I couldn't get the latex code right for the bottom line. However the bit i'm stuck on is the last line:

    b(a^j)(b^(−1)) = (bab^(−1))^j = (a^(−1))^j = a^(−j)

    If anyone can explain how the left progresses to the right hand side, in very obvious terms for me it would be great cause i can't see the woods for the trees atm.

    Rep awarded on this one

    b(a^j)(b^(−1)) = (bab^(−1))^j
    just try it:



    (bab^(−1))^j = (a^(−1))^j
    this follows from the group multilplication:
    in D8 you bab^(-1)=a^(-1)
Submit reply
Turn on thread page Beta
Updated: February 11, 2010
The home of Results and Clearing


people online now


students helped last year

University open days

  1. SAE Institute
    Animation, Audio, Film, Games, Music, Business, Web Further education
    Thu, 16 Aug '18
  2. Bournemouth University
    Clearing Open Day Undergraduate
    Fri, 17 Aug '18
  3. University of Bolton
    Undergraduate Open Day Undergraduate
    Fri, 17 Aug '18
Do you want your parents to be with you when you collect your A-level results?
Useful resources

Make your revision easier


Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here


How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.