Question

is anyone good with the topic groups and symmetries?

Answer 1

ask, you will probably get several answers

Answer 2

Let G be an abelian group with identity element 'e' an element of G and let n be a positive integer.
Show that the subset Gn = { g an element of G: g^n = 'e' } is a subgroup of G

Answer 3

for a fixed \(n\) right?

Answer 4

yeah fixed n

Answer 5

what do you need to show?
you need to show
a) \(e\) the identity is in there, and that is obvious yes?

Answer 6

you need to show
b) it is closed under inverses

Answer 7

e belonging because e^n=e

Answer 8

no we are actually showing Gn = { g an element of G: g^n = 'e' } is a subgroup of G

Answer 9

we have to find inverse

Answer 10

yes make sure you know what exactly you need to show

Answer 11

yeah so to show if something is a subgroup do we have to prove those 3 points? (associativity, identity, and inverse) ?

Answer 12

so yes it is

Answer 13

g^-1=g^2n

Answer 14

you do not need to prove it is associative, it inherits associativity from the operation in G

Answer 15

yes you should find if exist e and inv

Answer 16

@mahmit2012 i am kind of confused in what you are doing sorry but i understand the first line where we got g*g^(-1) = e

Answer 17

G is a abelian group so g-1 exsist

Answer 18

but everything you are doing after i do not know where you are getting g^(n+1) then g^(2n+1)