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Is this my mistake?

I am trying to solve

   Assuming[0 < a < 1 && 0 < b < 1 && 0 < c < 1 && 0 < n < 2 && Q > 0 && 
  0 < p <= 1 && Element[a | b | c | n | p | Q, Reals], 
 Reduce[2*a*b*n*c*Q - 3*a*b*n*p*c*Q + a*b*n*p^2*c*Q - 
    4*a^2*b*n*p*Q^2 - 4*a*b^2*n*p*Q^2 + 6*a^2*b*n*p^2*Q^2 + 
    6*a*b^2*n*p^2*Q^2 - 2*a^2*b*n*p^3*Q^2 - 2*a*b^2*n*p^3*Q^2 + 
    a^2*b*c*Q^2 + a*b^2*c*Q^2 - 2*a^2*b*p*c*Q^2 - 2*a*b^2*p*c*Q^2 == 
   0]]

However, the answer provided doesn't seem to be fit with my assumption. For instance, I clearly state that $0<p<=1$. But in the answer, it give me $p=2$, and also $p=0$. How do I filter out these unwanted values?

The program returns,

     (Q == 0 && (p == 1 || 
     p == 2)) || ((-c + 2 c p + 4 n p - 6 n p^2 + 2 n p^3) Q != 0 && 
   a == (2 c n - 3 c n p + c n p^2 + b c Q - 2 b c p Q - 4 b n p Q + 
     6 b n p^2 Q - 
     2 b n p^3 Q)/((-c + 2 c p + 4 n p - 6 n p^2 + 
       2 n p^3) Q)) || (p == 1/2 && n == 0 && Q != 0) || (Q == 0 && 
   2 - 3 p + p^2 != 0 && n == 0) || (Q == 0 && 
   n (2 - 3 p + p^2) != 0 && c == 0) || ((p == 1 || p == 2) && 
   c == 0 && Q != 0) || (n == 0 && -1 + 2 p != 0 && c == 0 && 
   2 p Q - 3 p^2 Q + p^3 Q != 0) || (p == 0 && n == 0 && c == 0 && 
   Q != 0) || (Q != 0 && p == 0 && 2 n != 0 && c == 0) || a == 0 || 
 b == 0 || Q == 0
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up vote 3 down vote accepted

Reduce has its own syntax for specifying constrains and domains.
Please try this:

Reduce[2*a*b*n*c*Q - 3*a*b*n*p*c*Q + a*b*n*p^2*c*Q - 
    4*a^2*b*n*p*Q^2 - 4*a*b^2*n*p*Q^2 + 6*a^2*b*n*p^2*Q^2 + 
    6*a*b^2*n*p^2*Q^2 - 2*a^2*b*n*p^3*Q^2 - 2*a*b^2*n*p^3*Q^2 + 
    a^2*b*c*Q^2 + a*b^2*c*Q^2 - 2*a^2*b*p*c*Q^2 - 2*a*b^2*p*c*Q^2 == 
   0 && 0 < a < 1 && 0 < b < 1 && 0 < c < 1 && 0 < n < 2 && Q > 0 && 
  0 < p <= 1, {}, Reals]
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