Recent content by esorey

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    Proof of Uniqueness of Non-Identity Commuting Element in D_2n

    Homework Statement If ##n = 2k## is even and ##n \ge 4##, show that ##z = r^k## is an element of order 2 which commutes with all elements of ##D_{2n}##. Show also that ##z## is the only nonidentity element of ##D_{2n}## which commutes with all elements of ##D_{2n}##. Homework Equations...
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    [Group Theory] Constructing Cayley Graph from Given Relations

    I figured it out! For some reason, I didn't realize that it didn't matter which two vertices you connect first, since from there you derive the rest. Thanks!
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    [Group Theory] Constructing Cayley Graph from Given Relations

    Homework Statement Show that there exists a group of order 21 having two generators s and t for which s^3 = I and sts^{-1} = t^2. Do this exercise by constructing the graph of the group.Homework Equations Based on the given relations, we have t^7 = I.The Attempt at a Solution Since ##s## and...