Recent content by NeoInTheMatrix

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    Question on Automorphism group as subgroup

    With that misunderstanding cleared up, the proof seems pretty straightforward:- Consider f in Auto(G). f is surjective and injective as well as homomorphic. The inverse f^-1 is surjective as well. Given any x in G, x = f^-1(f(x)) such that x is in the image of f^-1 since the image of f(x)...
  2. N

    Question on Automorphism group as subgroup

    I'll edit the question to move the -1 to the outside. I've never heard of f^-1 as something different from the inverse.
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    Question on Automorphism group as subgroup

    f is a homomorphism since it is part of the automorphism group of G. So therefore:- e' = f(e) = f(x x^-1) = f(x)f(x^-1) .. where e' is the identity in the image of f. But this means that f(x^-1) is f^-1(x) since we can also have e' = f(x^-1 x) = f(x^-1)f(x) by similar logic.
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    Question on Automorphism group as subgroup

    The problem is as follows:- Statement of the problem: Given group G, show that the automorphism group of G is a subgroup of the permutation group of G. I can show that Auto(G) is a subset of Perm(G) easily. So I have to show that subgroup conditions hold: (1) for each x in Auto(G), x inverse...
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    Express maximum as an equation

    For part 1, you can write a piecewise function but it is just typing out what maximum means. For the second part, you can't necessarily recover A from C. Suppose that B>A. Then A could be any value less than C.
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    What is the Limit of the Sequence {arctan(2n)} and Does it Converge to pi/2?

    Your other condition is that its monotonic increasing in n. And there's a theorem that says it converges to the sup of {arctan(2n): n>0}, which is pi/2.
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    GRE Math subject exam Prep- Pre-calc

    GRE Math subject exam Prep-- Pre-calc For those of you who are preping, or have taken it already, what did you use to prep for the pre-calc section of the GRE subject exam in math?
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    Do you view a theorem's proof as an exercise?

    Not doing the exercises in a math book is like not even bothering to read the book.
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