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    Cyclic groups

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    (a) Let F = { (matrix with first row; a 0, second row is 0 a) : a is an element of R

    Show that F is a field and that F ~= R

    (b) Give the definition of a cyclic group
    Prove that every subgroup H of a cyclic group G =<a> is itself cyclic

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    Solution Summary

    This is a proof regarding fields. The cyclic groups for modern algebra are examined.