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Abstract Algebra 9.3: Factor Groups

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  • เผยแพร่เมื่อ 11 ต.ค. 2018
  • In this video, we show how a normal subgroup can be used to create a group of cosets, which we call a factor group.

ความคิดเห็น • 21

  • @justinpearce6707
    @justinpearce6707 4 ปีที่แล้ว +11

    Hello Patrick. These videos don't have crazy view but they are easily the best abstract algebra 1 videos on this platform. I cannot thank you enough for these video lectures. You have managed to very quickly convey this information in a way that is extremely easy to understand. It is a shame that these videos are not getting thousands of views considering how incredible they are. Thank you again for taking the time to make these, they are exceptional.

    • @patrickjones1510
      @patrickjones1510  4 ปีที่แล้ว +6

      Thank you for the kind words. They mean a lot to me. Honestly, I'm surprised the videos have gotten as many views as they have. I made them when I got roped into teaching an abstract algebra course after the previous professor bailed at the last minute. The course was scheduled to be online (which I think is a horrible way to teach any course with this much theory), and I didn't have the option of changing it. I figured that if I had to create videos anyway, I may as well make them available for anyone that was willing to watch.

  • @ClumpypooCP
    @ClumpypooCP 9 หลายเดือนก่อน

    I really like the way youre teaching this. Not sure why, but it works for me. Thanks!

  • @yBazo82
    @yBazo82 3 ปีที่แล้ว

    this is very good, thanks

  • @TrucNguyen-co2pt
    @TrucNguyen-co2pt 3 ปีที่แล้ว

    The video is so good and easy to understand.Thank you!
    it would be better if you continue the video without breaking them into different parts or having a link to the next part somewhere....

    • @patrickjones1510
      @patrickjones1510  3 ปีที่แล้ว +1

      I'm glad you found the video helpful. I am no longer teaching an abstract algebra course, so I'm very unlikely to do any further work on these videos. However, there is a playlist which has all the videos in order, so that might help with your sequencing.

  • @aryankumarprasad1574
    @aryankumarprasad1574 3 ปีที่แล้ว

    Subbed

  • @TheTessatje123
    @TheTessatje123 ปีที่แล้ว

    Really great video!! Writing down the factor/quotient group in a table, makes it much easier to understand than how it's normally introduced!
    One question: Why is {R90, R270}=R270K 8:43? And similarly, {H, V}=VK 9:09?

    • @patrickjones1510
      @patrickjones1510  ปีที่แล้ว +1

      Remember that R270*K is the set which consists of each element of K multiplied by R270. K in the example is {R0,R180}, and R270*R0=R270, R270*R180=R90.
      The other one is similar, you just need to remember how the group operation works.

    • @TheTessatje123
      @TheTessatje123 ปีที่แล้ว

      @@patrickjones1510 Of course! Thanks for your quick response 🙂

  • @francisellec.largado6409
    @francisellec.largado6409 2 ปีที่แล้ว +1

    hello, can I ask if the quotient group is the same as the factor group?

    • @patrickjones1510
      @patrickjones1510  2 ปีที่แล้ว +1

      Yes, those are just two terms for the same thing.

  • @EpicOfficialUNNES
    @EpicOfficialUNNES 4 ปีที่แล้ว +1

    Why we do 0+H not 0xH?

    • @patrickjones1510
      @patrickjones1510  4 ปีที่แล้ว +1

      It is typical to use the symbol of the group operation. Since our group operation on the integers is addition, we just use the same notation.

    • @EpicOfficialUNNES
      @EpicOfficialUNNES 4 ปีที่แล้ว

      @@patrickjones1510 is only addition?

    • @EpicOfficialUNNES
      @EpicOfficialUNNES 4 ปีที่แล้ว

      Or we can use other operation

    • @patrickjones1510
      @patrickjones1510  4 ปีที่แล้ว

      @@EpicOfficialUNNES Multiplication is not a group operation on the integers, since it lacks inverses.

    • @EpicOfficialUNNES
      @EpicOfficialUNNES 4 ปีที่แล้ว

      @@patrickjones1510 what is group operation on integers?

  • @dineshprajapat9039
    @dineshprajapat9039 5 ปีที่แล้ว

    Sirr plzz aap Hindi m smja do na...