Question

find the unique subgroup of U(11) of order 5 and list its elements?

Answer 1

@mahmit2012

Answer 2

i have found that 3, 4, 5 , and 9 has order 5 but what does it mean by unique subgroup and list the elements

Answer 3

the other elements are not of order 5 correct?

Answer 4

nope 1 has order 1 , (2,6,7,8) has order 10 and those are the generators, (3,4,5,9) have order 5 and (10) has order 2

Answer 5

and 3,4,5,9 by themselves all generate the same group correct?

Answer 6

uhh what do you mean by that

Answer 7

the element 3 generates {1,3,4,5,9}

Answer 8

the element 4 generates {1,3,4,5,9}

Answer 9

...

Answer 10

i am confused by that how did you get those numbers :S

Answer 11

get which numbers?

Answer 12

where you said the element 3 generates {1,3,4,5,9}

Answer 13

i dont know what i am trying to find when it says find the unique subgroup of U(11) or order 5 and list its elements

Answer 14

3
3*3=9
3*9=5 mod 11
3*5=4 mod 11
3*4=1 mod 11

Answer 15

{3,9,5,4,1}

Answer 16

it is the unique subgroup of order 5

Answer 17

im sorry but i am still kind of confused a little ok so you know how i got (3,4,5,9) and it has order 5 right now are we picking any number in that set?

Answer 18

or are we going to do it for 4 5 and 9 as well

Answer 19

any number from that set generates the same group and all the other numbers beside 1 generates all of U(11)

Answer 20

alright so the unique subgroup of U(11) of order 5 are (3,4,5,9) ?

Answer 21

the unique subgroup of order 5 is {1,3,4,5,9}

Answer 22

1 is in the group

Answer 23

why are we including 1 though doesnt 1 have order 1

Answer 24

you are looking at the order of the group not the order of each of the elements.

Answer 25

oooo yeah yeah sorry ok

Answer 26

if you don't include 1 then your 'group' is not closed under the operation

Answer 27

your right my mistake