Abstract Algebra (orders of groups): U(3), U(4) U(12), etc
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pka
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Re: Abstract Algebra (orders of groups)
When posting an advanced question it is necessary to include definition of terms. I doubt that anyone not using your textbook has any idea what U(n) is as a group. It certainly is not a standard notation.
When posting an advanced question it is necessary to include definition of terms. I doubt that anyone not using your textbook has any idea what U(n) is as a group. It certainly is not a standard notation.
Re: Abstract Algebra (orders of groups)
U(n) was used as notation in my algebra class as the "set of positive integers less than n and relatively prime to n." It is a group under multiplication modulo n and has order Phi(n). However, pka is right, I have also seen this notation in studying advanced linear algebra to stand for another group (though I don't remember which), so it is not standard.
Movest, a theorem you might find useful: If m and n are relatively prime then Phi(mn) = Phi(m)Phi(n). And, of course if p is prime Phi(p)=p-1.
U(n) was used as notation in my algebra class as the "set of positive integers less than n and relatively prime to n." It is a group under multiplication modulo n and has order Phi(n). However, pka is right, I have also seen this notation in studying advanced linear algebra to stand for another group (though I don't remember which), so it is not standard.
Movest, a theorem you might find useful: If m and n are relatively prime then Phi(mn) = Phi(m)Phi(n). And, of course if p is prime Phi(p)=p-1.