Question

give an example of a group such that \(a^{-1}ba\neq b\)
Please, help

Answer 1

@kirbykirby

Answer 2

what group give us ab not equal to ba?

Answer 3

in other words, can you think of a non commutative group?

Answer 4

matrix

Answer 5

yep

Answer 6

matrix composition

Answer 7

a group is defined for associativity. only abelian groups are commutative.

i recall a 6 element group of matrixes that are not commutative with composition:

(fog)(x) not= (gof)(x)

Answer 8

what to call it tho ... i dont think dihedral is right, maybe Z2 x Z3 ?

Answer 9

I don't know .:) I am new in the field, try to come up with a new concept. :)

Answer 10

or was it 8 elements ... youll prolly have a clearer memory of it than i at the moment