Fun! Let's see. We have: ---------------------------- {0}, {1}, {5}, {6} {-1, 1}, {4, 6}, {1, 5} {-1, 1, 5} {-3, -1, 1, 3}, {-4, -1, 1, 4}, {-4, -2, 2, 4} {-3, -1, 1, 3, 5} {-4, -3, -2, -1, 1, 2, 3, 4} ---------------------------- Plus all the rest. —Dan
On Apr 20, 2016, at 6:30 PM, Allan Wechsler <acwacw@gmail.com> wrote:
Wait, I think I just realized. Consider, for instance, {2,4,6,8}. Under multiplication, these do form a group with identity 6. I didn't think of it because it doesn't "cohere" with the ring of integers mod 10. {5} is another example. I'm not sure how to enumerate these. {6} and {4,6} are two more.
Keith F. Lynch <kfl@KeithLynch.net <mailto:kfl@keithlynch.net>> wrote:
I meant any subset of {0,1,2,3,4,5,6,7,8,9} which forms a group under multiplication modulo 10.