#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: 6

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

Question 1:
Let p1:= 21534
p2:= 41235

What is p2*p1

Answer 1:
[32154]

Question 2:
Explain in your own words why if the order of pi is k
Then |GG({p1})| = k

Answer 2:

The permutation kind of resets when you generate perms after k times, so you get the same perms again and hence don't increase the number of perms, and hence |GG({p1})| = k

Question 3:
Prove that if H is a subgroup of a group G then

|G|/|H| is an integer

Answer 3:

If H is a subgroup then it is basically a subpart of size k. 

Question 4:
Who's theorem is it?

Answer 4:
Could not find it but to guess Coseys and Lagrange's Theorem

Question 5:
Generate a random permutation of length 9 and by hand finds its cycle

Answer 5:
[[9, 2, 8, 7, 6, 5, 1, 3, 4]]
Same as PtoC

Question 6:
Check that the range of FunF over all permutation of length 7

Answer 6:
Maple did not like what I did