Order of Elements in a Group | Abstract Algebra

We introduce the order of group elements in this Abstract Algebra lessons. We'll see the definition of the order of an element in a group, several examples of finding the order of an element in a group, and we will introduce two basic but important results concerning distinct powers of elements with finite order and elements with infinite order. #abstractalgebra #grouptheory
Permutation Groups: • Infinite Order Element...
Finding the Order of Group Elements: • Finding the Order of G...
Finite Powers of an Element are Distinct: • Proof: Finite Order El...
Infinite Order Elements have Distinct Powers: • Infinite Order Element...
Abstract Algebra Course: • Abstract Algebra
Abstract Algebra Exercises: • Abstract Algebra Exerc...
◉Textbooks I Like◉
Graph Theory: amzn.to/3JHQtZj
Real Analysis: amzn.to/3CMdgjI
Proofs and Set Theory: amzn.to/367VBXP (available for free online)
Statistics: amzn.to/3tsaEER
Abstract Algebra: amzn.to/3IjoZaO
Discrete Math: amzn.to/3qfhoUn
Number Theory: amzn.to/3JqpOQd
★DONATE★
◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits: / wrathofmathlessons
◆ Donate on PayPal: www.paypal.me/wrathofmath
Thanks to Petar, dric, Rolf Waefler, Robert Rennie, Barbara Sharrock, Joshua Gray, Karl Kristiansen, Katy, Mohamad Nossier, and Shadow Master for their generous support on Patreon!
Thanks to Crayon Angel, my favorite musician in the world, who upon my request gave me permission to use his music in my math lessons: crayonangel.bandcamp.com/
Follow Wrath of Math on...
● Instagram: / wrathofmathedu
● Facebook: / wrathofmath
● Twitter: / wrathofmathedu
My Math Rap channel: / @mathbars2020

[@WrathofMath]

I previously had a video on this, but I used a needlessly complicated definition which made the lesson a few minutes longer than it needed to be. So I redid it.

[@keldonchase4492]

Thanks for the videos; they are immensely helpful!!!
Question about the example presented at 4:40:
The way I look at it is:
Cycle 1:
Start with 1:
1 --> 6 (1)
6 --> 4 (2)
4 -> 2 (3)
2 -> 1 (4)
I started with 1 and ended with 1 so to get back to 1, I had to make 4 “jumps” so 4 is a possible answer for our order.
Cycle 2:
Skip all the numbers covered in Cycle 1 so I start with 3.
3 --> 3 (0)
Since 3 maps to itself, I do not consider a “jump”.
0 would be a possible answer but since it is non-positive, I can eliminate it as a possibility.
Cycle 3:
5 --> 5 (0)
Again, not a “jump” because 5 maps to itself.
Again, 0 can be eliminated as a possibility since it is non-positive.
So that is why the order is 4.
Is this way of thinking correct or is there something important I’m missing?
Thank you!!

[@mgyodzs1]

Good explanation! Keep going, You do good job.

[@WrathofMath]

Thanks, will do!

[@HorenKriz]

So helpful thanks

[@WrathofMath]

Thanks for watching!

[@summerhunt77]

Thank you.

[@WrathofMath]

Glad to help!

[@iraqi-ff9690]

Thank u so much 🖤

[@WrathofMath]

You're welcome!

[@punditgi]

You can never go wrong with Wrath of Math!

[@WrathofMath]

Such is the order of things!

[@user-eu4xt1rx6b]

very interesting

[@WrathofMath]

I think so too!

[@jialinding9636]

The frog is the icing on the cake.

[@WrathofMath]

It always is!

[@naruhitoabiku9451]

i love you

[@InoceramusGigas]

Hi W.O.M
Would love some videos on ramsey theory!
Could be a great fit in your graph theory playlist, or just within a general combinatorics theme.
There is definitely room for a more intuitive explanation on CZcams.
Love the Abstract algebra vids.