Question

has anyone dealt with group theory?

Answer 1

heard of it
why?

Answer 2

you need a proof of something?

Answer 3

yes
it says prove or disprove: |xy|=|x|*|y| for x,y are in G. and i know that it isnt true but im running stuck on how to show it.

Answer 4

where G is a group

Answer 5

i am not sure what the question is
for a Group you need a set and an operation
what is the set? what is the operation?

Answer 6

i was going to show that the inverses are not the same because inverses are unique and then there they are not the same

Answer 7

operation is multipilication

Answer 8

what is G?

Answer 9

it is a general Group it doesnt specifiy. Bc obviously with some groups that would hold but not all.

Answer 10

oooh i bet \(|x|\) means the order of \(x\) right?

Answer 11

yeah correct

Answer 12

so x^n=e

Answer 13

where e is the identity

Answer 14

then it is not true by example
suppose |G|=6 which would contain an element \(x\) of order 3 and \(y\) of order 2
then |xy|=1

Answer 15

btw for disprove an example is sufficient

Answer 16

i think i follow i am still trying to understnad the whole concept.

Answer 17

yep thanks.

Answer 18

think of the group \(\mathbb{Z}_3\times \mathbb{Z}_2\)

Answer 19

thanks