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...
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[@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!!

[@MrCoreyTexas]

I was wondering why not 0 for the order, and the reason it is not 0 is because every element to the 0th power is the identity element, so it has to be a positive integer to be non trivial

[@mgyodzs1]

Good explanation! Keep going, You do good job.

[@WrathofMath]

Thanks, will do!

[@summerhunt77]

Thank you.

[@WrathofMath]

Glad to help!

[@jialinding9636]

The frog is the icing on the cake.

[@WrathofMath]

It always is!

[@HorenKriz]

So helpful thanks

[@WrathofMath]

Thanks for watching!

[@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!

[@iraqi-ff9690]

Thank u so much 🖤

[@WrathofMath]

You're welcome!

[@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 KZbin. Love the Abstract algebra vids.

[@naruhitoabiku9451]

i love you

[@nyxiiestelle]

am i the only one who couldn't understand this 😭😭? I'm feeling very dumb, i watched it so many times and still can't get it well idk why🥹!! ( I'm a math major)