Group Theory Notes

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Group Theory Notes01234567Donald L. KreherMarch 18, 2020iiAckowledgementsI thank the following people for their help in note taking and proof reading:Mark Gockenbach, Ryan McNamara, Kaylee Walsh, Tjeerd What is a Group ? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Some properties are unique. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . When are two groups the same?.

(ii)if ba= ca, then b= c. 1.2. SOME PROPERTIES ARE UNIQUE. 7 Then (G;) must be a group. Also provide a counter example that shows that this is false if Gis in nite. 4.Show that the Latin Square e g 1 g 2 g 3 g 4 g 5 g 6 g 1 e g 3 g 5 g 6 g 2 g 4 g 2 g 3 e g 4 g 1 g 6 g g g g 1 g g g g g 1 1