Thread: Lagranges theorem

Originally Posted by adam_leeds

the inverse of -1 is -1 and is in the set

1 times -1 = -1 which is in the set which shows closure

but i thought you said 1 couldnt be in the subset?

No - the subset cannot be precisely if it is trivial, but 1 must be in it.

Originally Posted by Swlabr

No - the subset cannot be precisely if it is trivial, but 1 must be in it.

so the non trivial subgroups are

{1,-1}
{1,i}
{1, -i}

{1,-1,i}
{1,-1,-i}

Originally Posted by adam_leeds

so the non trivial subgroups are

{1,-1}
{1,i}
{1, -i}

{1,-1,i}
{1,-1,-i}

No. Remember what the theorem you are trying to show says. Which of your sets don't adhere to what it says?

The problem with some of your given sets is closure: .

Originally Posted by Swlabr

No. Remember what the theorem you are trying to show says. Which of your sets don't adhere to what it says?

The problem with some of your given sets is closure: .

bottom two because -1 * 1 * i = -i which is not in the subgroup

-1 * 1 * -i = i which is not in the subgroup

Originally Posted by adam_leeds

bottom two because -1 * 1 * i = -i which is not in the subgroup

-1 * 1 * -i = i which is not in the subgroup

Yes, but you just multiply two elements together and not all of them. The product of any two elements in the set must be in the set.

Originally Posted by Swlabr

Yes, but you just multiply two elements together and not all of them. The product of any two elements in the set must be in the set.

i love you, cheers for your help