We provide these examples to help you get started.
Problem 1. Let be a group, such that . Find the order of .
Solution
From .
Proceeding in this manner (You should prove this with a lemma), we find that , positive integer.
Thus
But
So , and therefore, .
Problem 2. Let be a group, such that . Prove that .
Proof
We have seen that , for positive integer.
We are looking for the smallest integer, such that
Now
But
So , and therefore, .
-
- Active Topics
-
-
- by Eli 19 minutes ago All in One: YouTube, TED, X, Facebook and Instagram Reels, Videos, Images and Text Posts View the latest post Replies 279 Views 6533
- by Eli 12 hours ago Russia Invades Ukraine View the latest post Replies 643 Views 209059
- by Eli 13 hours ago Collection of Greatest Christian Hymns of all Times View the latest post Replies 30 Views 42695
- by Eli 1 day ago Chat With ChatGPT - An Interactive Conversational AI View the latest post Replies 21 Views 22692
- by Eli 5 days ago Re: What is in Your Mind? View the latest post Replies 658 Views 271380
- by Eli 6 days ago Mission Control Live: NASA InSight Mars Landing Live Coverage View the latest post Replies 32 Views 12962
- by Eli 6 days ago Christian Podcasts View the latest post Replies 4 Views 28282
- by Eli 1 week ago Python Packages for Scientific Computing View the latest post Replies 7 Views 2713
- by Eli 1 week ago Pondering Big Cosmology Questions Through Lectures and Dialogues View the latest post Replies 32 Views 44706
- by Eli 2 weeks ago C++ PROGRAMMING CRASH COURSE View the latest post Replies 4 Views 1292
-
Order of an Element in a Group - Solved Examples
-
- Information
-
Who is online
Users browsing this forum: No registered users and 2 guests