Permutation Groups and Symmetric Groups | Abstract Algebra

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We introduce permutation groups and symmetric groups. We cover some permutation notation, composition of permutations, composition of functions in general, and prove that the permutations of a set make a group (with certain details omitted). #abstractalgebra #grouptheory
We will see the Cayley table for the symmetric group S3, and look at some inverse permutations. We also cover the definition of a permutation, which is a bijection from a set to itself.
Cayley's Theorem: • Proof of Cayley's Theo...
A proof that compositions of bijections are bijective in two parts:
• Proof: Composition of ...
• Proof: Composition of ...
Abstract Algebra Course: • Abstract Algebra
Abstract Algebra Exercises: • Abstract Algebra Exerc...
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Опубликовано:

27 сен 2024

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Комментарии : 44

@WrathofMath Месяц назад

Support this course by joining Wrath of Math to access exclusive and early videos, original music, plus lecture notes at the premium tier! ru-vid.com/show-UCyEKvaxi8mt9FMc62MHcliwjoin Abstract Algebra Course: ru-vid.com/group/PLztBpqftvzxVvdVmBMSM4PVeOsE5w1NnN Abstract Algebra Exercises: ru-vid.com/group/PLztBpqftvzxVQNtNnXeHB_1yquKUY98Xz

@Adecto 11 месяцев назад

In the first 3 minutes I understood everything better than after 4 hours of lectures and hours of watching other RU-vid videos. Thank you so much!!!

@NicholasBrogle 7 месяцев назад

Retweet

@area51xi Год назад

These are some of the best math videos on YT. Other math YT-ers should take note. Aside from good content: 1. high resolution, 2. good mic/clear audio, 3. clear annotations. Not sure why others can't just buy a good microphone and put it by their mouth rather than putting it across the room, in their waving hand, in the kitchen sink, not plugging it in, handing it to their crying baby....

@WrathofMath Год назад

Thanks so much! Though it took me nearly 6 years to be making the videos this high quality, it's all a learning process!

@misterentername8869 Год назад

These are amazing explanations, clear and mentions everything! Thank you, this deserves more views.

@WrathofMath Год назад

Thank you, that's precisely what I've been trying to achieve with the Abstract Algebra videos. Lots more to come in the playlist: ru-vid.com/group/PLztBpqftvzxVvdVmBMSM4PVeOsE5w1NnN

@namelessflower7 5 месяцев назад

Thank you! You made everything so easy to understand.

@benallen9112 9 месяцев назад

alpha is its own inverse because it is a transposition. i.e., any 2 cycle is its own inverse. The cycle decomposition of alpha is (1 2)(3) = (1 2). Hence, (1 2) is its own inverse as is any other transposition. Hope this helps anyone else studying for their abstract algebra final!

@prianborah Год назад

Hi, this is a fantastic video. Could you make a video on A4 discrete symmetry group and its character table and what its irreducible representations like 1,1',1'', and 3 means, and also its multiplication table??

@tirtahadith 2 месяца назад

Done (but i think i need to rewatch it again multiple times

@ParvejBiswas-qi4re 4 месяца назад

Such a great math❤ explanation ❤

@xibbit6322 4 месяца назад

my teachers making us do fuunction composition from left to right because he prefers it but no one uses that... its so annoying and confusing :(

@Bertilsdotter1 Год назад

Very good explained... Big thanks

@WrathofMath Год назад

Glad to help - thanks for watching!

@SagnikSaha-v1n 7 месяцев назад

Thank you amazing video.

@WrathofMath 7 месяцев назад

Thank you!

@bryanherrera9549 5 месяцев назад

Thank you!

@WrathofMath 5 месяцев назад

You're welcome!

@backiyalakshmi5990 9 месяцев назад

Thank you so much sir

@WrathofMath 9 месяцев назад

Most welcome!

@danielrosen4496 Год назад

Wondering if Set is infinite,

@WrathofMath Год назад

Which set? I'm not sure what your question is. If you're asking if there are infinite permutation groups, the answer is yes. For example, one permutation on the reals might swap the positives and negatives and keep 0 fixed.

@turefu8681 Год назад

Thanks a lot for this explanation. It helps me with a problem troubling for two days.

@WrathofMath Год назад

Glad to help! Check out my playlist if you're looking for more abstract algebra! ru-vid.com/group/PLztBpqftvzxVvdVmBMSM4PVeOsE5w1NnN

@MYTHBuSS Год назад

Please Solve This Problem!! My Maths Teacher Asked me to Prove that For Area of Square =, 1/2 x d x d Please help 😌🔥

@homqua9613 9 дней назад

Thanks so much, your explanation is clear 💛

@WrathofMath 8 дней назад

Glad to help, thanks for watching!

@mzarinchang3744 7 месяцев назад

Thats so cool....I thought that if a=a^(-1) then a must be the identity.......but this example showed that its not neccessarily true.....

@ismailadekunle1978 Год назад

Thanks so much for his video❤

@WrathofMath Год назад

Thanks for watching!

@estherlevenson1835 7 месяцев назад

Thank you so much. I'd like to know more about the relationship between symmetry groups and permutation groups.

@jaydevdeshmukh3831 7 месяцев назад

In your table at the end of the video, Why does Beta and Beta lead to delta? Should it also not have identity there? Same goes with Delta and Delta which is giving Beta.