Recent content by ti89fr33k

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    Kernel of a field homomorphism

    Show that the kernel of a field homomorphism is either the trivial homomorphism or isomorphic to the field. I've tried to see it as a factor group, but I'm stuck. Can someone help? mary
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    Natural Group Homomorphism in Action

    What is it, and can you give me a few examples of how its used? Thanks, Mary
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    Log n < O(n^ε) for Large n - Simple Function Growth

    oh...i see...
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    Log n < O(n^ε) for Large n - Simple Function Growth

    log n^epsilon/2 has to grow slower than n^epsilon?
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    Log n < O(n^ε) for Large n - Simple Function Growth

    there is a pure algebra method
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    Log n < O(n^ε) for Large n - Simple Function Growth

    yes, but my instructor specifically mentioned not to use l'hopitals rule
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    Log n < O(n^ε) for Large n - Simple Function Growth

    The answer is quite intuitive...but i want a rigorous method
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    Log n < O(n^ε) for Large n - Simple Function Growth

    I know the limit is 0...but how do you evaluate it?
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    Log n < O(n^ε) for Large n - Simple Function Growth

    Show log n < O(n^epsilon) for n sufficiently large. Not actually calculus, but it has something to do with limits, so there. :smile: Thanks, Mary
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    Can All Subgroup Permutations in S_n Be Even or Half Even?

    I've solved the first two...now about the last one NVM: i made tons of mistakes, leading to an erroneous result.
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    Can All Subgroup Permutations in S_n Be Even or Half Even?

    For the last one, I experimented with various sizes of \sigma. The others I have no idea how to approach (please do not spoonfeed, just give hints). Thanks, Mary
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    Can All Subgroup Permutations in S_n Be Even or Half Even?

    Hello, I am a student at CMU, enrolled in the Abstract Algebra class. I'm having trouble with a few problems, see if you can figure them out. Show that for every subgroup $J$ of $S_n|n\geq 2$, where $S$ is the symmetric group, either all or exactly half of the permutations in $J$ are...
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