/sci/ - Science & Math

[Anonymous No.3705850]

Hey /sci/

Need some help on group theory.

I need to find a subgroup of U(Z_2007) with an order of 6.
Now, Through some guessing i found that the subgroup brought forth by 893 works (893^6 mod 2007 = 1 and 893^n with n<6 doesn't give 1 mod 2007).

However, i have no idea how i do this generally, like i said, i got it through guessing.

[Anonymous No.3706130]

I'm a physicist and I don't know why it works but here is some information:

2007 = 3*3*223

then you have

http://www.wolframalpha.com/input/?i=Table[Mod[223^n%2C+2007]%2C+{n%2C+1%2C+10}]

i.e. 223^n = {1,223,892,1561}

and all these numbers plus one seem to generate groups in your sense.
223^m mod 2007 is Z_2
and the other two are your group with 6 elements.

[Anonymous No.3706880]

hurrdurr

[Anonymous No.3706978]

The order of a subgroup divides the order of the group.
6 does not divide 2007, so no such subgroup exists.