Number of cyclic subgroups of order 15 in Z_90 (+) Z_36
- To: mathgroup at smc.vnet.net
- Subject: [mg37986] Number of cyclic subgroups of order 15 in Z_90 (+) Z_36
- From: "Diana" <diana53xiii at earthlink.remove13.net>
- Date: Sat, 23 Nov 2002 19:15:45 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Mathematica groupies, I just got my copy of Mathematica tonight. I understand permutations of S_5 and A_5, etc., but I am having a little difficulty figuring out how to calculate the order of elements of Z_90 and Z_36, and the order of elements of the external direct product of Z_90 (+) Z_36. I am wanting to calculate the number of cyclic subgroups of order 15 in Z_90 (+) Z_36 with Mathematica. Z_90 is the additive group {0, 1, 2, 3, ..., 89}. Z_36 is the additive group {0, 1, 2, 3, ..., 36}. So, elements of Z_90 (+) Z_36 would be 2-tuples of the form: (a, b), where a is an element of Z_90, and b is an element of Z_36. If you add (a, b) to itself 15 times, you will get {0, 0}. Note that the operation of adding the first component of the 2-tuple is modulo 90, and the operation of adding the second component of the 2-tuple is modulo 36. Can someone help? Thanks, Diana M.