#ATTENDANCE QUIZ FOR LECTURE 10 of Dr. Z.'s Math454(02) Rutgers University


# Please Edit this .txt page with Answers


#Email  ShaloshBEkhad@gmail.com 
#Subject: p10
#with an attachment called
#p10FirstLast.txt
#(e.g. p10DoronZeilberger.txt)


#Right after finishing watching the lecture but no later than Oct. 9, 2020, 8:00pm




THE NUMBER OF ATTENDANCE QUESTIONS WERE:


PLEASE LIST ALL THE QUESTIONS FOLLOWED, AFTER EACH BY THE ANSWER


1. What is p2 * p1? 


A: 32154, this is not the same as p1 * p2


2. Explain in your own words why if the order of pi is k then |GG({pi})|=k 


A: Because the function outputs the subgroup generated by a positive integer n and a set of permutations in {1,...,n} 


3. Prove that if H is a subgroup of a group G then |G| / |H| is an integer 


If H is a subgroup of a group G, then H is contained within G. 
Therefore, every element of H is an element of G.
So, the nops(H) > nops(G), and nops(G) is divisible by nops(H). 
So it is proven that |G| / |H| is an integer 


4. Whose theorem is it? 


Leonardo?


5. Generate a random permutation of length 9 and by hand find its cyclic representation. 


randperm(9);
[3, 8, 4, 9, 1, 5, 6, 7, 2]


Cycles are (1349287651)
6. Check that the range of FunT over all permutations of length 7


This made my computer crash, but I was able to confirm that FunT yields the same results as permute(7), which is the set of all permutations of 7.