10 abstract algebra proofs = our third take home midterm in the abstract algebra class. on the test it stated you are allowed to use your notes, the course textbook, and old homework. you are also allowed to talk to the instructor. you are not allowed to use other books, or to talk to anyone else about the exam (including the TA).

there’s one problem on the test, i originally thought i did it correctly but since the teacher talked specifically about the definition of the problem today in class, i know i got it wrong. just to make sure, i asked him to look at my proof. he confirmed my proof is not correct. the notation i used for the commutator subgroup seemed familiar to him. he asked me where i got that. i seriously had came up with that myself. it’s nothing too fancy. they defined the set that generated the commutator subgroup to be
{xyx^-1y^-1 : x,y in G}
and usu. conjugate is written by ghg^-1 for g in G. in this case, i will have to write something like gxyx^-1y^-1g^-1 which is very messy so i wrote as g[x,y]g^-1 where [x,y] stands for xyx^-1y^-1. the teacher said he guessed i’ve seen a proof in our course textbook considering the commutator subgroup. i seriously did NOT. but since he mentioned it to me, i checked the textbook out. now i found a proof in our textbook proving the EXACT PROBLEM on the take home test. it blowed my mind. apparently if i have seen this proof beforehand, why would i bother asking him if i got the problem right or wrong. but OMG, how there can be an answer in the textbook to the problem on the test when we are allowed to use the textbook?!

i felt so weird that i emailed the teacher:
On Apr 14, 2004, at 1:10 PM, Ying Zhang wrote:
> since it’s stated on the test
> that we are allowed to use the course textbook, this shouldn’t be
> considered cheating, should it?

No. It’s not cheating. When I assigned the problem I didn’t realize the proof was in the book, however.

But you are allowed to use anything in the book that you want.