Select Page

(a) Show that the relations a^4 = 1, b^2 = a^2 and b^(-1)ab = a^(-1) define a group of order 8. (It is called the quaternion group.)(b) Show that this group is not isomporphic to Î4 (also of order 8).Please see the attachment for more precise text description.We have the definition of quaternion group as follows.We also have anther non-abelian group with order 8. The group is called dehedral group defined as with the following definition.Now I claim that and are not isomorphic.
Actually, we only need to check the number of elements with order 2.
In , it only contains one element with order 2. Since , then we have , then , . Then both and has order 4. We note that . Thus only has one element that has order 2.
In , at least we have two elements and that have order 2.
Therefore, and are not isomorphic.You can visit the link http://www.math.kent.edu/~white/41001/order8sub.pdf to know more detailed structures of the two groups.

#### Why Choose Us

• 100% non-plagiarized Papers
• 24/7 /365 Service Available
• Affordable Prices
• Any Paper, Urgency, and Subject
• Will complete your papers in 6 hours
• On-time Delivery
• Money-back and Privacy guarantees
• Unlimited Amendments upon request
• Satisfaction guarantee

#### How it Works

• Click on the “Place Order” tab at the top menu or “Order Now” icon at the bottom and a new page will appear with an order form to be filled.
• Fill in your paper’s requirements in the "PAPER DETAILS" section.
• Fill in your paper’s academic level, deadline, and the required number of pages from the drop-down menus.
• Click “CREATE ACCOUNT & SIGN IN” to enter your registration details and get an account with us for record-keeping and then, click on “PROCEED TO CHECKOUT” at the bottom of the page.
• From there, the payment sections will show, follow the guided payment process and your order will be available for our writing team to work on it.