Abstract Algebra, Lec 10A: Euclidean Algorithm, Subgroup Lattices, Permutation Groups

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(0:00) Sample Exams.
(0:25) Lecture topics.
(1:04) Euclidean algorithm. Example: use the Euclidean Algorithm to find gcd(9900,4158) and write it as a linear combination of 9900 and 4158 (as 9900s + 4158t).
(11:18) Subgroup lattice of S4 (the symmetric group on 4 objects), including the alternating group A4 (consisting of even permutations in S4).
(18:47) Subgroup lattices for Z27 and Z15.
(23:27) Permutations and permutation groups.
(26:45) The symmetric group Sn.
(28:33) Example: S3. Write the 3! = 6 elements in array notation, and mention that a 3-cycle and a 2-cycle (transposition) can be used to generate the group.

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Thank you Professor for these wonderful lectures. As a student pursuing undergrad Math on my own. these are a blessing. Thank you.

saquibmohammad

2:50 Terminology : 9900 is the dividend, 4158 is the divisor, 2 is the quotient and 1584 is the remainder

WahranRai

Thank you ♥️
Love from kolkata, India 🥀

subhadipsarkar

I have seen some papers on algebraic geometry where a theorem states "There is an algorithm that does such and such with this specific complexity". Well, existence of an algorithm for something is definitely worth proving, considering that we have many problems for which no algorithm is know, and even some that are proven to be undecidable, thus no algorithm exists. I have not read the book, but I think the division algorithm theorem is of this kind, saying something of the sort "Given a and n, there is an algorithm to find q and r such that a = qn + r, where 0 <= r < n."

lucasvella

Pleased to get you sir, it is wonderful, love and respect from Pakistan 🇵🇰

BrilliantPkF

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