basic examples with groups -- Abstract Algebra Examples 3

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When filling in a Cayley table, it's sometimes nice to use associativity: if you notice that 2*2=4, and you're doing the row for 4 after the row for 2, you can just say a*4=(a*2)*2, and put each element through the 2 row twice instead of doing the calculation. Saves some taking remainders as you get down the table and it's nice for getting an intuition as to what associativity means for Cayley tables.

iabervon
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Thank you for your great work as usual! 🙂 Some little mistakes in the video though. On the first example, the term "ac" is missing when you expand a*(b+c+bc). Regarding the multiplication table, you are missing a "13" line... Perhaps you are superstitious? 😉 There is also a small error when multiplying the matrices. It should be "a+x" not "a+y".

laurentwatteau
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[5:28] Minor error: The Cayley table is missing 13 on the left-hand column.

GlenMacDonald
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After noticing that the Cayley table has every element listed once and only once in each row and column, I fell down in the Sudoku group theory rabbit hole.

scottmiller