The Student Room Group
Uni students - Complete our survey >>
Uni students - Complete our survey >>
Uni students - Complete our survey >>

Group Theory Fp3 Question?

IMG_0399.jpgHow do you know 6 is the identity element in Q2g?
Reply 1
Avatar for alow
alow
19
Original post by swagmister
IMG_0399.jpgHow do you know 6 is the identity element in Q2g?


If {G,∘}\{ G,\circ \} is a group then the identity, I∈GI \in G, is the element for which:

I∘g=g ∀g∈GI\circ g=g \: \forall g \in G
(edited 7 years ago)
Reply 2
Avatar for swagmister
swagmister
OP
11
Original post by alow
If GG is a group with operation ∘\circ then the identity, II is the element in GG for which:

I∘g=g ∀g∈GI\circ g=g \: \forall g \in G


Okay so I just do trial and error? My teacher said for the tables to see which one where the row and coloumn matched up but it doesn't seem to work in this case
Reply 3
Avatar for alow
alow
19
Original post by swagmister
Okay so I just do trial and error? My teacher said for the tables to see which one where the row and coloumn matched up but it doesn't seem to work in this case


Yeah for small groups just draw the group table and see which element follows that rule.

If it doesn't work, you've made an arithmetic error.
(edited 7 years ago)
Reply 4
Avatar for math42
math42
20
Original post by swagmister
IMG_0399.jpgHow do you know 6 is the identity element in Q2g?


2 * 6 = 12 so 2 O 6 = 2
4 * 6 = 24 so 4 O 6 = 4
etc.
Original post by alow
If {G,∘}\{ G,\circ \} is a group then the identity, I∈GI \in G, is the element for which:

I∘g=g ∀g∈GI\circ g=g \: \forall g \in G


You also need g∘I=g ∀g∈Gg\circ I=g \: \forall g \in G
Reply 6
Avatar for alow
alow
19
Original post by EricPiphany
You also need g∘I=g ∀g∈Gg\circ I=g \: \forall g \in G


I know :tongue:

But that group is Abelian so I didn't want it to make it any more complicated and confusing.
Original post by alow
I know :tongue:

But that group is Abelian so I didn't want it to make it any more complicated and confusing.


oh, didn't look
Reply 8
Avatar for swagmister
swagmister
OP
11
Original post by alow
Yeah for small groups just draw the group table and see which element follows that rule.

If it doesn't work, you've made an arithmetic error.


I get now thanks 👍
IMG_0401.jpg441.8KB
Reply 9
Avatar for swagmister
swagmister
OP
11
How I go about finding the identity for h? IMG_0402.jpg
Reply 10
Avatar for math42
math42
20
Original post by swagmister
How I go about finding the identity for h? IMG_0402.jpg


Should be kinda obvious. Think about it, it's an additive group
Original post by 1 8 13 20 42
Should be kinda obvious. Think about it, it's an additive group


Ah I get it it's 0👍

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you