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Topic:  structure of (Z/p^k)^* 
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Subject:  structure of (Z/p^k)^* 
Author:  sequos 
Date:  Sep 27 2003 
you may know, that for odd primes p the above mentioned group is cyclic.
for example Z/3^2 has 6 units and they are generated by 5: 5, 5^2 = 7, 5^3 = 8,
5^4 = 4, 5^5 = 2, 5^6 = 1 mod 9.
the big exception is p=2. here for k >= 3 the things change:
for k=3 we must have 4 units and there are only 3 kandidates to generate our
group of units:
3, 5, 7.
but we have 3^2 = 1, 5^2 = 1, 7^2 = 1.
one can show, that in the case p=2 and k>=3 we have
(Z/2^k)^* = {+1} X C, where C is a cyclic group of
order 2^(k2).
my question to all is now: let K : Q_2
be a 2adic numberfield with dimension n = ef over
the 2adic numbers, let A be the ring of whole numbers of K and let P be its
maximal ideal, what ist then the
structure of
(A/p^k)^* ?
thanks 4 any answer
sequos
 
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