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MidPrep - H is a finite subset of a group G and H is...

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M IDTERM TOPICS Please make sure you are able to prove (from scratch) that the subgroup of Z generated by two integers a and b is equal to the subgroup of Z generated by the single integer gcd( a,b ) . You should also be able to apply this theorem to show that the equation ax + by = n has an integral solution ( x,y ) if and only if n is a multiple of gcd( a,b ) . Also, please make sure you are able to prove that if
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Unformatted text preview: H is a finite subset of a group G and H is closed under the binary operation of G , then H ≤ G . Needless to say, there will be other questions on the exam as well. .. so make sure you study the above two enough that you don’t have to spend too much time on them during the test. 1...
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