Question

Give an example of group elements a and b with the property that a^-1ba does not equal b

Answer 1

Well... one thing's for sure, we can't have an abelian group...

Answer 2

yes, i realized this. I need an answer

Answer 3

We can use any group?

Answer 4

I'm assuming. That is all of the question.

Answer 5

What are some of the non-Abelian groups you're familiar with?

Answer 6

D4 is the only one we have covered in class so far but we are covering another one on monday

Answer 7

D4 is fine... what are its elements?

Answer 8

(I'm asking you because I don't know what you guys call the elements of D4)

Answer 9

there are 8 elements, the 4 rotations, horizontal, vertical, and the two diagonals

Answer 10

or at least that is what I gathered from the lesson

Answer 11

Okay.. hang on...

Answer 12

thank you!

Answer 13

Let's consider a diagonal rotation along the \ diagonal as a
and a rotation 90 degrees clockwise as b.

Answer 14

ok....

Answer 15

Sorry, I meant a diagonal *reflection*

Answer 16

If a is the diagonal reflection along the \ diagonal (not the other / one)
Then what is \(a^{-1}\)?

Answer 17

i have no idea. What is a Math Processing Error?

Answer 18

I meant a^-1

Answer 19

If a is the diagonal reflection along \, then what is its inverse?

Answer 20

I don't know. I thought for the example the question wanted actual numbers for the elements.

Answer 21

do you know of any non-abelian group?

Answer 22

Just D4.