MAT-3110 Midterm: MATH 3110 App State Fall2013 Midterm

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15 Feb 2019
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Be sure to show your work! (a) let s = (0, 1] = {x | 0 < x 1}. Then s is not a group under multiplication. List the group axioms which hold and then using concrete counterexamples, show the other axioms fail. Axioms that fail: (b) let e be the set of even integers. What are they? (c) draw the subgroup lattice for z75. [note: 75 = 3 52. : (13 points) permutations (a) what is the order of = (142)(235)(13)(25)? (b) let = (134)(24)(12). Find 1. (c) write = (1572)(2345)(12) as a product of transpositions. Is even / odd (d) let = (12345)(67). Then compute 111 1: (9 points) dihedral problem. (a) draw a regular hexagon and label the re ective symmetries: v1, v2, . , v6 (moving around the hexagon in the counter-clockwise direction). Also, let r60 be the counter-clockwise rotation of 60 .

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