Recent content by iamalexalright

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    Proof of Cyclic Subgroup Equivalence for Finite Groups

    Yeah, I see that now... Well, its obvious that <a> is contained in <b> Not sure how I can use the fact that a and b have the same order to prove the other direction, any hints?
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    Proof of Cyclic Subgroup Equivalence for Finite Groups

    Homework Statement Suppose a \in <b> Then <a> = <b> iff a and b have the same order (let the order be n - the group is assumed to be finite for the problem). Proof: Suppose a and b have the same order (going this direction I'm trying to show that <a> is contained in <b> and <b> is...
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    Proving the Inclusion of <a> in H: A Permutation Group Proof

    shameful bump
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    What Is the Correct Way to Differentiate xe^2x?

    Close but you are missing one thing. Maybe if you saw another example it would become more clear... What is the derivative of sin(2x)? Or if you prefer by the definition of the chain rule: (f \circ g)' = f'(g) * g' In your case, what is f and what is g? Then can you see your mistake?
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    What Is the Correct Way to Differentiate xe^2x?

    Nope ! Here we have to use the chain rule but before we get there, what is the derivative of e^(x)?
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    What Is the Correct Way to Differentiate xe^2x?

    Not correct: First, what is the derivative of e^(2x) ? Second, if f and g are arbitrary functions of x, what is the derivative of f*g with respect to x (ie, what does the product rule say)?
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    What Is the Correct Way to Differentiate xe^2x?

    you'll have to use the product rule AND the chain rule
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    Proving the Inclusion of <a> in H: A Permutation Group Proof

    Homework Statement Suppose G is a group, H < G (H is a subgroup of G), and a is in G. Prove that a is in H iff <a> is a subset of H. Homework Equations <a> is the set generated by a (a,aa,aa^-1,etc) The Attempt at a Solution For some reason this seems too easy: 1. Suppose a...
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    Abstract Algebra - Subgroup of Permutations

    Homework Statement A is a subset of R and G is a set of permutations of A. Show that G is a subgroup of S_A (the group of all permutations of A). Write the table of G. Onto the actual problem: A is the set of all nonzero real numbers. G={e,f,g,h} where e is the identity element...
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    Proving H as a Subgroup of G: Using the Abelian Property

    Homework Statement G is an abelian group Let H = {x \in G : x = x^{-1} Prove H is a subgroup of G. I have two methods in my arsenal to do this (and I am writing them out additively just for ease): 1. Let a,b be in H. If a + b is in H AND -a is in H then H<G. or 2.Let a,b be in H...
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    Graduate Free Group with defining equations

    So today in class we talked about defining equations... We were asked to consider the group generated by <a,b> with the defining equations a^2 = e, b^3 = e, and ba = ab^2. With these equations we can easily see that there can only be a maximum of 6 elements (and apparently most of the...
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    GCD of ab,c = 1: Implications for a & b

    oh wow, that is painfully obvious ... thanks Char. Limit !
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    GCD of ab,c = 1: Implications for a & b

    Homework Statement If gcd(ab,c) = 1 then gcd(a,c)=1 and gcd(b,c)=1 2. The attempt at a solution Well, if gcd(ab,c) = 1 we know that abk + cl = 1 for some integers k and l not really sure where to go from here... any hints?
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    Dirac Delta Integral Homework: Proving Equations

    Homework Statement For some reason these are just messing me up. I need to prove: 1. \delta(y)=\delta(-y) 2.\delta^{'}(y) = -\delta^{'}(-y) 3.\delta(ay) = (1/a)\delta(y) In 2, those are supposed to be first derivatives of the delta functions Homework Equations Use an integral...
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    Triple Integral Evaluation for Bounded Region with Polynomial Boundaries

    Just started using wolframalpha.com for the integrals. Just wanted to make sure my syntax and what not was correct. Have to draw it out to get the limits heh