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Two starting programming questions re alternating groups and EulerPhi LCM numbers

• To: mathgroup at smc.vnet.net
• Subject: [mg37912] Two starting programming questions re alternating groups and EulerPhi LCM numbers
• From: diana53 at earthlink.net (Diana)
• Date: Tue, 19 Nov 2002 03:51:29 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

Mathematica junkies...
 
I have ordered Mathematica Student, and am excited about starting to
program with it.
 
I was wondering if someone with experience could help me with two
(easy?) programs to get started.
 
Program 1:
 
A. I want to first list the elements of A_5. These would be the even
permutations of S_5, such as:
 
(1, 2, 3, 4, 5)
(1, 2, 4, 3 5), etc. There are 60 of these.
 
B. Secondly, I want to figure out how to compute the order of each of
the elements.
 
C. Last, I want to create a Cayley table of 60 x 60 elements, i.e.,
(1, 2, 3, 4, 5) * (1, 2, 4, 3, 5). This would be the answer you get to
first permuting a 5-tuple by (1, 2, 3, 4, 5), and then permuting it by
(1, 2, 4, 3, 5).
 
I have done all of this with an Excel spreadsheet, and am not turning
this in or getting credit for it. Just want to know how to do it.
 
Program 2
 
I understand that Mathematica has the EulerPhi function in it. Does
anyone know how to get the program to list the elements which are less
than and relatively prime to any given "n"?
 
Thanks,
 
Diana

• Follow-Ups:
  • Re: Two starting programming questions re alternating groups and EulerPhi LCM numbers
    • From: Tomas Garza <tgarza01@prodigy.net.mx>