AIM Chat with Bill Abrams , Chirashree Bhattacharya , Anne Collins , Benjamin Collins , Dennis Keeler, Edward Moy , Julianne Rainbolt , Jen Roche , Daniel Shown , Gordon Swain , Brian Walter , Gordon Williams , Shaochen Yang , Daylene Zielinski .
10:01 AM
Russell Blyth: hi again
Julianne Rainbolt: hi
Dennis Keeler: hi
Julianne Rainbolt: we had to restart chat - please close the old chat
Gordon Swain: I'm chatting on all cylinders now!
Julianne Rainbolt: vnc is back up
Julianne Rainbolt: we had to restart chat - please close the old chat
Tom Hoffman has joined this chat.
Russell Blyth: video is up
Russell Blyth: OK, a little chaotic here this am
Daniel Shown: video is up rtsp://165.134.240.35/GAP060713am1.sdp
Russell Blyth: We do have three projects ready to go and even a volunteer group to go first
10:05 AM
Russell Blyth: Is anyone having problems?
Shaochen Yang: http://www2.muw.edu/~syang/Course/CayleysTheorem.pdf
Benjamin Collins: Say something, Russell.
Julianne Rainbolt: anyone having with VNC or QT?
Brian Walter: my QT just froze
Benjamin Collins: Mine, too.
Julianne Rainbolt: yes it did here too
Bill Abrams: me too
Julianne Rainbolt: we are restarting
Russell Blyth: It went down
Gordon Williams: wow... major technicals this morning
Russell Blyth: 
Julianne Rainbolt: 
Russell Blyth: OK, we'll be up in a second
Benjamin Collins: Hey, I'm just happy it's not just me.
Daniel Shown: video is up rtsp://165.134.240.35/GAP060713am1.sdp
Russell Blyth: Quit and restart QT
Julianne Rainbolt: we are going to start with Brian, Shoachen and Daylene's project!
Daylene Zielinski: This first part was mine.
Daylene Zielinski: You can skip Ex. #1
10:10 AM
Daylene Zielinski: I'm hoping students will say that they see the group is abelian and each non-identy elmt has order 2.
Daylene Zielinski: My QT just froze
Brian Walter: there goes QT again
Anne Collins: mine too
Russell Blyth: Yes, it just quit for some reason, we're rebooting
Russell Blyth: Sorry about this
Benjamin Collins: When we get to it... What is "AsGroup"?
Daylene Zielinski: It checks if a set forms a group, but checking the multiplication for all the group properties.
Julianne Rainbolt: it changes a an algebraic object into a group (if it can)
Daylene Zielinski: If your set is not a group, it returns, "fail".
Daylene Zielinski: Otherwise, it retruns a set of generators.
Julianne Rainbolt: and after using this command you can then use built in functions for groups
10:15 AM
Julianne Rainbolt: (such as IsAbelian, Factor, etc)
Dennis Keeler: I think it displays a set of generators, but returns the group itself.
Tom Hoffman: It returns the group, not the generators.
Russell Blyth: Will be the same address when it comes back
Russell Blyth: We seem to have a corruption in the Broadcasting software
Daylene Zielinski: Sorry -- sloppy languge on my part.
Russell Blyth: So we are reinstalling it
Dennis Keeler: yikes!
Gordon Swain: Is it smart emough to recognize what operation is implied?
Russell Blyth: Stand by
Bill Abrams: You think the system was frightened by all this math?
Russell Blyth: (It would not let us send audio when we restarted)
Tom Hoffman: yes, it uses the natural operation on the elements
Russell Blyth: Maybe!
Russell Blyth: So, continue with the discussion in chat
Dennis Keeler: I've only seen AsGroup used on permutations or subsets of groups.
Russell Blyth: It seems to be going well
Daylene Zielinski: My original plan was to have the students use GAP to make the multiplication table for the four permutations and check for "groupness" from the table, but AsGroup seemed more natural at this point in a first semester course.
Gordon Swain: Are there other ways to describe elements, other than perms?
Julianne Rainbolt: You can create an set and then define and multiplication table for it and then use AsGroup to treat this set as a group
Daylene Zielinski: What do you mean?
Anne Collins: ooh! that's what we want! how?
Gordon Swain: As an array?
Julianne Rainbolt: yes Gordon - when we are back I will show you an example
Bill Abrams: You can put the multiplication table in as a Magma.
Dennis Keeler: Besides perms, it seems GAP naturally contains finite field elements and invertible matrices over those elements.
Gordon Swain: What is a "Magma"?
Julianne Rainbolt: i will do the example without sound while we are waiting
10:20 AM
Dennis Keeler: I don't think we've seen any other internally understood examples.
Bill Abrams: A set with a binary operation. Uve to unfortunately the set seems to have to be m1,m2,... They claim it is a Bourbaki term.
Gordon Swain: Can integers mod n be entered like 0 mod 5, 1 mod 5, etc?
Daylene Zielinski: Very cool!
Bill Abrams: If you just do IsAbelian or IsCyclic with m, will it fail?
Russell Blyth: We're switching computers and have broadcast up
Gordon Williams: what do the lists correspond to?
Julianne Rainbolt: i just did an example of creating a magma, giving the binary operation using a multiplication table and then turned it into a group.
Russell Blyth: It means we won't have the same video archive, though
Gordon Williams: ahh
Julianne Rainbolt: the lists are describing the multiplication table
Dennis Keeler: if I understand, if you do Display(MultiplicationTable(g)); you will get the matrix a. Correct?
Julianne Rainbolt: let's try it
Julianne Rainbolt: yes it works
Russell Blyth: We''ll work on the problem and see if we can get everything working for the pm
Russell Blyth: Can everyone see and hear?
Benjamin Collins: I can.
Gordon Swain: That's cool. So you could build tables and see if they are groups.
Bill Abrams: So far.
Russell Blyth: RIGHT
Tom Hoffman: good here
Russell Blyth: oops
Daylene Zielinski: good here
Gordon Swain: Can you use a pair to define a Ring?
10:25 AM
Benjamin Collins: Can you Display(MultiplicationTable(m)); ?
Russell Blyth: Yes
Gordon Swain: "a" was the Magma, not "m"
Tom Hoffman: a is just the table
Bill Abrams: a was the matrix = multiplication table.
Benjamin Collins: I don't really understand "Magma". Is this a major lack on my part?
Dennis Keeler: a was a matrix. Then m was the Magma made from the matrix (or table)
Gordon Swain: Oops, my mistake
Bill Abrams: Magma is just a set with a binary operation.
Gordon Williams: any axiomatic requirements?
Benjamin Collins: Is this a term actually used, or just in GAP?
Bill Abrams: Not according to the manual.
Tom Hoffman: it is used in some books
Gordon Williams: Magma (algebra) - Wikipedia, the free encyclopedia
Gordon Williams: so also known as a groupoid
Gordon Williams: which I was familiar with (vaguely)
Dennis Keeler: someone asked if one can make a Ring via multiplication tables
Bill Abrams: The manual claims it is a Bourbaki term.
Julianne Rainbolt: switching QT to am2
10:30 AM
Julianne Rainbolt: we will go back to S,D and B's project now
Benjamin Collins: I don't believe in Wikipedia. It's not in the Wolfram Math World site, so I don't accept it.
Russell Blyth: Video is up
Bill Abrams: Sorry, I worship Bourbaki so I have to accept it.
Gordon Williams: I find Wikipedia is pretty good on technical stuff, but grain of salt taken as needed
Daniel Shown: rtsp://165.134.240.35/GAP060713am2.sdp
Julianne Rainbolt: any QT or VNC problems - we are starting their project now
Daylene Zielinski: No need
Daylene Zielinski: Well, the students would, I don't know if we really need to.
10:35 AM
Daylene Zielinski: I had in mind to use the permutations.
Gordon Williams: question about that... is your notation convection that (123) => 1->2->3->1 or 3->2->1->3... cause I'm confused by your hint
Gordon Williams: convention
Julianne Rainbolt: this first
Julianne Rainbolt: the first
Julianne Rainbolt: am I right Daylene?
Daylene Zielinski: I think so.
Daylene Zielinski: yes
Daylene Zielinski: Yeah!
10:40 AM
Daylene Zielinski: The group in table 3 and the group of permutaions are iso.
Daylene Zielinski: Yup
Daylene Zielinski: So, the group in table 3 is iso to a subgp of S_6.
Daylene Zielinski: We can leave this as an exercise.
Daylene Zielinski: Yes
Daylene Zielinski: The importance of moving to D_4, is that D_4 is not abelian, and our first two examples were.
Daylene Zielinski: Also the students have to number the elements on their own this time.
Daylene Zielinski: Now, Shaochin's part starts.
Shaochen Yang: Use the first example to formulate the proof.
Shaochen Yang: skip the proof
Daylene Zielinski: Brian -- Your turn
10:45 AM
Brian Walter: let's rock!
Benjamin Collins: Do I have a handout for Brian?
Brian Walter: mine is the third part of this handout
Benjamin Collins: Gotcha.
Daylene Zielinski: Shaochin, can you post the link again?
Julianne Rainbolt: I'll repeat the url (it is what russell showing):http://www2.muw.edu/~syang/Course/CayleysTheorem.pdf
Brian Walter: yes, my instructions are more open-ended than daylene's
Brian Walter: obviously the students will have seen D4 already, since it's the main example in Gallian Chapter 1
Brian Walter: but i like asking them to think about it again as a review
10:50 AM
Daylene Zielinski: Russ, Brian's asking the students to view R_90 and H as permutations of the corner labels.
Brian Walter: in the interests of time, we could just note that we know how this will work out...
Daylene Zielinski: So, R_90 is (1,2,3,4)
Daylene Zielinski: MT QT just froze again.
Julianne Rainbolt: it's ok here
Brian Walter: i think H is (1,2)(3,4) in this case
Benjamin Collins: My QT is OK.
Dennis Keeler: ok here
Shaochen Yang: ok here
Daylene Zielinski: I'm back up.
Brian Walter: uh-oh - VNC froze
Daylene Zielinski: Mine too.
Bill Abrams: There it goes.
Gordon Swain: VNC gone
Russell Blyth: See if it came back
Brian Walter: i can connect - do something
10:55 AM
Benjamin Collins: I got it back.
Julianne Rainbolt: it's back
Dennis Keeler: yes, back
Brian Walter: yes, it's back
Russell Blyth: We're having a weird am
Daylene Zielinski: Make GAP the top window, please.
Daylene Zielinski: THz
Brian Walter: originally i had thought to have them make GAP do the work and then ask them to think about this
Brian Walter: but i couldn't figure out a straightforward way to have GAP do the work
Brian Walter: the next-to-last question, i mean
Daylene Zielinski: Just use Order(SymmetricGroup(3));
Brian Walter: anyway, i'd then want them to think about it (and it's obvious anyway)
Daylene Zielinski: Good use of conjugations.
Brian Walter: right-o; we can take a conjugate of D4
Gordon Swain: For the previous questions (in general) could you look at homomorphisms and see that all are trivial?
Brian Walter: nice idea, gordon
11:00 AM
Gordon Swain: Or at least have nontrivial kernel
Brian Walter: but they don't know about homomorphisms yet, i think
Daylene Zielinski: Yes
Brian Walter: absolutely
Gordon Swain: That was serious stuff!
Dennis Keeler: http://pascal.mth.muohio.edu/keelerswain.pdf
Julianne Rainbolt: onto Dennis and Gordon S's project!
Russell Blyth: VNC stays up, hopefully
Dennis Keeler: Since sending, we added a question 6 to Project 1, so might want to download again
Russell Blyth: OK
Russell Blyth: Can we try through iChat
Russell Blyth: ?
Edward Moy has left this chat.
Daniel Shown: rtsp://165.134.240.35/GAP060713am3.sdp
Daniel Shown: video is up
Russell Blyth: DK, can you send new version in iChat?
Dennis Keeler: It's athttp://pascal.mth.muohio.edu/keelerswain.pdf
Edward Moy has joined this chat.
Dennis Keeler: don't really need the new version
Julianne Rainbolt: by the way bill and edward - i did get your emai
Julianne Rainbolt: l
Dennis Keeler: It just has a question 6 which asks them to conjecture that the size of a conjugacy class divides the order of the group
11:05 AM
Bill Abrams: ?sophus
Bill Abrams: Sorry, that was supposed to be typed in GAP
Bill Abrams: I am interested in Lie Algebras and saw that in the titles.
Gordon Swain: Probaly just do the D6 stuff.
Gordon Swain: Use List(ConjugacyClasses(d6),Elements): to do it all at once
Edward Moy has left this chat.
Gordon Swain: I didn't tell the students this, they may figure that oout themselves
11:10 AM
Gordon Swain: Can replace Elements with Size
Daylene Zielinski: There you go Anne!
Gordon Swain: you mean it doesn't like Elemnts?
Anne Collins: great then i can spell "centre" right!
Gordon Swain: I do that all the time
Edward Moy has joined this chat.
Julianne Rainbolt: Edward - are you doing ok?
Edward Moy: I'm fine at the moment.
Gordon Swain: Yes
Dennis Keeler: I imagined they'd know Abelian groups, yets
Dennis Keeler: yes
Dennis Keeler: But otherwise, might only know of D_{2^n} as a non-abelian eg
11:15 AM
Dennis Keeler: Something like Order(Center(d4));
Dennis Keeler: But s4 is not a p-group.
Dennis Keeler: Sorry it wasn't clear. I was just thinking they would think of d4 at least.
Dennis Keeler: yeah, go on ahead
Dennis Keeler: couldn't think of an easier way to get intereesting p-groups
Dennis Keeler: yes, typo. Yes, use
Dennis Keeler: G:=SylowSubgroup(s8,2);
Dennis Keeler: sorry
Dennis Keeler: for s8, the p=3,5,7 groups are abelian
Dennis Keeler: yes, that's why the last exercise is for S_10
11:20 AM
Dennis Keeler: certainly not going to get all p-groups, but will get some that are hard to build.
Tom Hoffman: this is a quick way to get nontrivial examples
Dennis Keeler: Like in Exercise 4. You can skip this. We're running short on time
Dennis Keeler: For example, the G in Exercise 3 is (D8 x D8) : C2
11:25 AM
Dennis Keeler: Yeah, I was hoping they'd do enough examples to get about any possible power of p except 1.
Gordon Swain: That was the previous conjecture at the end of part one.
Dennis Keeler: Nope, I'm good.
Tom Hoffman has left this chat.
Gordon Swain: Want to look at the Conjugacy classes for Z12?
Julianne Rainbolt: 
Julianne Rainbolt: "Laboratory Experiences in Group Theory - A Manual to be Used With Exploring Small Groups"
Daniel Shown: http://unr.sedu/homepage/keppelma/fgb.html
Julianne Rainbolt: by Ellen Maycock Parker
Dennis Keeler: Typo abovehttp://equinox.unr.edu/homepage//keppelma/fgb.html
11:30 AM
Daniel Shown: oops
Daniel Shown: sorry about that.
Daniel Shown: thanks Dennis
Dennis Keeler: Group Explorer may be good too
Dennis Keeler: http://groupexplorer.sourceforge.net/
Daylene Zielinski: FYI: The first 4 pages and last page of our Cayley's Theorem project are available as Word documents if anyone is interested.
Benjamin Collins: I sent something to Juli's e-mail. We're ready whenever.
Julianne Rainbolt: DK - thanks
Russell Blyth: ok Ben - we'll do that one after lunch too
Gordon Williams: lunchtime now right?
Russell Blyth: yes
Russell Blyth: video down
Russell Blyth: after lunch - Finite Group Behavior and
Bill Abrams has left this chat.
Russell Blyth: more group projects
Daylene Zielinski has left this chat.
Julianne Rainbolt: Bye all!
Shaochen Yang has left this chat.
Julianne Rainbolt: and thanks!
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Chirashree Bhattacharya has left this chat.
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Russell Blyth: vnc going down
11:35 AM
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