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 2005-09-18, 09:12 #1 DSC   Aug 2005 7 Posts abstract algebra please help me with this horrible problem anyone, thanks! Determine the subgroup lattice for Zp^n, where p is prime and n is some positive integer.
2005-09-18, 13:48   #2
R.D. Silverman

Nov 2003

26·113 Posts

Quote:
 Originally Posted by DSC please help me with this horrible problem anyone, thanks! Determine the subgroup lattice for Zp^n, where p is prime and n is some positive integer.

I trust that you really mean Zp^n and not GF(p^n).

The integers co-prime to p^n form a multiplicative group mod p^n.
The integers mod (say) p^n-1 do not form a group mod p^n.

I don't understand what you mean by "sub-group lattice'

 2005-10-04, 09:14 #3 geoff     Mar 2003 New Zealand 13×89 Posts I think the subgroup lattice of a group G is the graph where the vertices are the subgroups of G and an edge joins H to K whenever K is a subgroup of H.

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