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    Normal subgroup with prime index

    Homework Statement Prove that if p is a prime and G is a group of order p^a for some a in Z+, then every subgroup of index p is normal in G. Homework Equations We know the order of H is p^(a-1). H is a maximal subgroup, if that matters. The Attempt at a Solution Suppose H≤G and...
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    Exchange for math and physics undergrad Rice and UC Berkeley advice

    Hello everyone, This is my second year as a physics, math double major, and I am an international student (not in the US). For 2012 fall and 2013 spring (or maybe just fall, I don't exactly know the policies, but I know I can do it multiple times), I plan to go to UCB as an exchange student...
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    PDE-initial condition

    PDE--initial condition Homework Statement Solve the equation u_x+2xy^2u_y=0 with u(x,0)=\phi (x). Strauss PDE 2nd ed., chapter 1.5, exercise 6. Homework Equations The question is under "Well-Posed Problems" section, so this might be about existence, uniqueness, or stability. The...
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    Fitzpatrick Advanced Calculus-edition differences

    Fitzpatrick Advanced Calculus--edition differences Hello everyone, I will buy Fitzpatrick's Advanced Calculus 2nd edition, but am not sure paperback or hardcover. The reason I'm unsure is that even though we should be using the international student edition, the professor is using the...
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    Philosophy of Science in Steampunk

    hi everyone-- for the philosophy of science course, I am planning to write a paper, and wanted to hear opinions about my topic. I am not a philosophy student (math&physics), and haven't taken that much of philosophy courses, so I can't go real deep about any subject, but I want to apply what...
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    Summer research program applications

    Hi everyone-- I am an international student, a sophomore currently, and for the summer I am applying for a few research programs in the States. I am trying to write the short essays for the applications nowadays, where most of them ask about "why would you like to participate in this...
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    Advices for a career in high energy physics

    Hi everyone-- This is my first post here, and I don't want this thread to look one of those that is created on every forum resulting on google, helplessly seeking help. I have been reading this forum for some time, and I guess I can ask for some academical advice and guidance. I believe it is...
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