Abstract Algebra. How to multiply permutations in cycle notation

Title: Abstract Algebra. How to multiply permutations in cycle notation
Abstract: I explain how to multiply permutations using cycle notation.
This video accompanies pages 32-37 of the class notes (www.math.colos...) for an "Introduction to Abstract Algebra" class (www.math.colos...)

[@ritwikpriyadarshi961]

Thank you! Could not multiply properly before this in cycle form and always had to turn into mappings, this is gonna save a lot of time :)

[@HenryAdamsMath]

Yes, you can multiply in cycle form (to save space).

[@johanlouisgouws3628]

Absolute GOAT in maths. Thank you so much

[@HenryAdamsMath]

Happy to help!

[@riyakeerthana3136]

Thank u for ur crystal clear explanation

[@HenryAdamsMath]

You're most welcome!

[@MasiKarimi]

Thanks a lot for the info! Awesome teaching!

[@HenryAdamsMath]

You are welcome!

[@sangavi2305]

Competent teacher👏👏👏well explainer👍

[@HenryAdamsMath]

Thank you! 😃

[@isthisbadbnumber]

thank you so much 🫶🏻

[@HenryAdamsMath]

You are welcome!

[@yourali1568]

Thank you form kuwait ❤️❤️

[@HenryAdamsMath]

You are welcome!

[@anuradhaupadhyay3258]

Well explained ❤❤ thank you sir

[@HenryAdamsMath]

Thanks!

[@kassembardan1601]

Very good method Bravoo many thx

[@HenryAdamsMath]

Thank you!

[@samiaurin2354]

Thank you so much! It helped me a lot to do my homework.

[@HenryAdamsMath]

You're welcome!

[@abigailhall51]

this was such a great explanation thanks loads from Manchester :)

[@HenryAdamsMath]

Wonderful, thanks, you bet!

[@kressmax]

Very well done!

[@HenryAdamsMath]

Thank you very much!

[@AlexD-wd6jx]

Great explanation, much appreciated!

[@HenryAdamsMath]

Glad it was helpful!

[@alamdarshah8595]

helped alot .... thank you...

[@HenryAdamsMath]

You are welcome!

[@まつまつ-x1f]

Awesome explanation!

[@HenryAdamsMath]

Thank you!

[@teachercomment801]

Thank you so much sir!

[@HenryAdamsMath]

You bet!

[@07.not.out.msd.]

Great work man!🔥

[@HenryAdamsMath]

Thanks!

[@naveenkumar-wo5yx]

Very nice explanation

[@HenryAdamsMath]

Thank you!

[@ezrakim1323]

This is sooo amazing🔥🔥🔥

[@HenryAdamsMath]

Thanks!

[@Alexander-tw2kw]

Thanks a lot for the explanation. If we're given a permutation, how do we find all permuations that commute with it?

[@HenryAdamsMath]

You may be interested in the page math.stackexchange.com/questions/4296033/all-permutations-that-commute-with-a-cycle

[@Alexander-tw2kw]

@@HenryAdamsMath thank you!

[@이재헌-e2o]

Love you professor!!

[@BairdBanko]

Permutations are awesome!

[@HenryAdamsMath]

I agree!

[@sehrish3444]

Great explanation ❤️😍

[@HenryAdamsMath]

Glad you think so!

[@azizyosri2058]

thank you so much !

[@HenryAdamsMath]

You are welcome!

[@vadiquemyself]

but why do you compose them right-to-left? I do it so : (1 2) + (2 3) = (1 2 3) and not the inverse (3 2 1) as it would be for (2 3) + (1 2) = (3 2) + (2 1) or don't u 🤔 ..... your example looks particularly commutative (1 4 3 2) + (1 3) + (2 4) also sums to (1 2 3 4) when (1 4 3 2) is done first

[@HenryAdamsMath]

I am also composing right to left, so the permutation on the right acts first!

[@Bagunka]

Great video as always! Also now you look younger than a year ago!

[@HenryAdamsMath]

Haha, thank you!

[@wenyaoma260]

It is very helpful! Thanks to your video!

[@HenryAdamsMath]

Great, I'm glad it was helpful!

[@kostper]

These look so fun to solve. Great explanation btw! You saved me because my notes are horrible.

[@HenryAdamsMath]

Happy to help!

[@rtk3738]

Thank you!

[@HenryAdamsMath]

You're welcome!

[@gustavocortico1681]

Is there a way to find "canonical" permutations? That is, the minimum number of functions that can be composed to give all the possible permutations on a finite set?

[@HenryAdamsMath]

Great question! I would refer you to the table on the second page of Keith Conrad's notes kconrad.math.uconn.edu/blurbs/grouptheory/genset.pdf. You can generate S_n with all transpositions, which is a set of size (n choose 2). But that is overkill. Alternatively, you can get away with only n-1 well-chosen transpositions. But that is again overkill. It turns out that the transposition (1,2) and the n-cycle (1,2,3,...,n-1,n) suffice to generate S_n (for all n >= 3) ! Those notes also describe some other ways to generate S_n with only two elements. You may also be interested in the following links: mathoverflow.net/questions/24101/natural-generating-sets-for-symmetric-groups www.mathcounterexamples.net/generating-the-symmetric-group-with-a-transposition-and-a-maximal-length-cycle/ www.jstor.org/stable/2974644

[@gustavocortico1681]

Thank you very much for the content! I will read this

[@sarkarsubhadipofficial]

Thank you❤️

[@HenryAdamsMath]

Certainly, you bet!

[@lordnk3698]

thank you very much

[@HenryAdamsMath]

Glad it helped!

[@hydose1]

@10:28 actually 3 goes back to 1 based on the left cycle.

[@incizor1273]

Thanks a lot sir!

[@HenryAdamsMath]

Most welcome!

[@miyamotomusashi4556]

Thanks a lot!

[@HenryAdamsMath]

You're welcome!

[@stanleeleo9019]

Thank you !

[@HenryAdamsMath]

You're welcome!