Re: Number of cyclic subgroups of order 15 in Z_90 (+) Z_36
- To: mathgroup at smc.vnet.net
- Subject: [mg38002] Re: Number of cyclic subgroups of order 15 in Z_90 (+) Z_36
- From: "Diana" <diana53xiii at earthlink.remove13.net>
- Date: Mon, 25 Nov 2002 01:56:54 -0500 (EST)
- References: <arp6l1$1rg$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Andrzej, Thanks for your help with this question! Two questions: 1. If I want to print out the elements of S which have order 15, do I use a nested If or Do loop? 2. I have just ordered the Mathematica Link to EXCEL package. I will use it to print out the Cayley Table you e-mailed for A_5. I have not been able to find a way to get all of the output of the table to print on Mathematica. I have tried page wrap of various sorts. Is there a way? Thanks for your time, you have made my Abstract Algebra experience so much more fun. Diana "Diana" <diana53xiii at earthlink.remove13.net> wrote in message news:arp6l1$1rg$1 at smc.vnet.net... > 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. > > >