My Math Forum  

Go Back   My Math Forum > Math Forums > Math

Math General Math Forum - For general math related discussion and news


Reply
 
LinkBack Thread Tools Display Modes
May 17th, 2017, 02:27 PM   #1
Adm
Newbie
 
Joined: May 2017
From: Neverland

Posts: 7
Thanks: 0

[Set Theory] - filling tablet

(G, *) is a group of 4 elements, a,b,c,e are different elements of G and e is a neutral element in (G, *).
given this equation: a*b = c*c
how can i start filling the tablet of (G, *) ?

i've understood that the column and row of the neutral element are just the same as the one that goes with it, a*e=a same goes to b,c and e.

and then i have this " every element in a tablet of a group can show only once in each row or column.

and can i assume that if a*b = c*c then b*a = c*c as well?
i'll appreciate any help or clues
Adm is offline  
 
May 17th, 2017, 03:22 PM   #2
Senior Member
 
Joined: Aug 2012

Posts: 1,661
Thanks: 427

Quote:
Originally Posted by Adm View Post
(G, *) is a group of 4 elements, a,b,c,e are different elements of G and e is a neutral element in (G, *).
given this equation: a*b = c*c
how can i start filling the tablet of (G, *) ?

i've understood that the column and row of the neutral element are just the same as the one that goes with it, a*e=a same goes to b,c and e.

and then i have this " every element in a tablet of a group can show only once in each row or column.
Get started by writing down the elements that you know.

Quote:
Originally Posted by Adm View Post
and can i assume that if a*b = c*c then b*a = c*c as well?
No, the group isn't Abelian unless the problem says it is. Now in some cases we can assume commutativity. For example if $xx^{-1} = e$ then we can conclude that $x^{-1}x = e$ as well. But in general you can't assume commutativity.
Maschke is online now  
May 17th, 2017, 04:27 PM   #3
Math Team
 
Joined: Jan 2015
From: Alabama

Posts: 2,878
Thanks: 766

There are only two groups, up to isomorphism, of order 4, the rotation group and Klein four group and they are both Abelian.
Country Boy is offline  
May 18th, 2017, 05:43 AM   #4
Adm
Newbie
 
Joined: May 2017
From: Neverland

Posts: 7
Thanks: 0

Quote:
Originally Posted by Maschke View Post
Get started by writing down the elements that you know.
maybe.jpg

[attached a picture]

so i've put all the Given one's first, then i start like this:
c*a can't be equal to a or c, because that'll make a or c nuetral elements which is wrong (Given that e is nuetral), niether can be a*b cuz it's already exist in the row so c*a = b.

and then c*b = a, because it's the only element left (no element duplicating)

and a*c = b because, a already exists in the row so it can't be, niether a*b or c (no duplicating) so we're left with b.

then can i assume that c*c = a*b = e (nuetral element) ?
because Given that G only Has 4 elements and e is the nuetral one within them, and it's the only one left in this row.

is that's the way ?
Adm is offline  
May 21st, 2017, 07:16 AM   #5
Adm
Newbie
 
Joined: May 2017
From: Neverland

Posts: 7
Thanks: 0

may anyone look up my answer please
Adm is offline  
May 21st, 2017, 09:49 AM   #6
Senior Member
 
Joined: Aug 2012

Posts: 1,661
Thanks: 427

Quote:
Originally Posted by Adm View Post
may anyone look up my answer please
Could you notate what you've got? Does't have to be fancy.
Maschke is online now  
May 26th, 2017, 01:48 PM   #7
Adm
Newbie
 
Joined: May 2017
From: Neverland

Posts: 7
Thanks: 0

Talking

thanks guys i've got it in the end !
Adm is offline  
Reply

  My Math Forum > Math Forums > Math

Tags
filling, set, tablet, theory



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Doing maths on a tablet Darrel Math Software 0 September 13th, 2015 04:18 AM
Filling a tank nathan Pre-Calculus 1 August 29th, 2014 04:23 PM
math software for pen tablet computers? math42 Academic Guidance 2 July 20th, 2011 01:59 PM
Math program for Tablet PCs (preferably freeware/opensource) Relinquished New Users 2 September 7th, 2007 07:02 PM





Copyright © 2017 My Math Forum. All rights reserved.