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    Mathematica: How do I program this? Square free part of an integer

    I am attempting to program Mathematica to multiply the square free terms of an integer. Basically say we are looking at 252, its prime factors are 2^2*3^2*7. So what I want to do is have Mathematica return to me just 2*3*7 when I enter 252. So I have this S := FactorInteger[252]...
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    Abstract Algebra: Finding Conjugates

    Yes. For take the identity element, I^-1*A*I=A So A is a conjugate of A, and likewise B is a conjugate of itself.
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    Orthogonal vectors

    Use the linearity of the dot product ( , ) so, (x,u)=(u,x)=0 and (x,v)=(v,x)=0, So consider, (u-v,x)=(u,x)-(v,x)=0 => (x,u-v)=0.
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    Field of order p^2

    This is an application of the Frobenius endomorphism if I am not mistaken,
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    Abstract Algebra: Finding Conjugates

    For conjugates of A, G={I, A, B, C, D, K} I^-1*A*I=A B^-1*A*B=D*C=K C^-1*A*C=C*B=K D^-1*A*D=B*K=C K^-1*A*K=K*D=C So K and C are conjugates of A. Do same procedure to find conjugates of B.