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Ball 153 | An Application of Cosets to the Rubik’s Cube 155Exercises 156Biography of Joseph Lagrange 1618 External Direct Products 162Definition and Examples 162 | Properties of External Direct Products 163 | The Group of Units Modulo n as an External Direct Product 166 | Applications 168Exercises 174Biography of Leonard Adleman 180Supplementary Exercises for Chapters 5–8 1819 Normal Subgroups and Factor Groups 185Normal Subgroups 185 | Factor Groups 187 | Applications of Factor Groups 193 | Internal Direct Products 195Exercises 200Biography of Évariste Galois 20799708_fm_ptg01_hr_i-xiv.indd 506/06/12 9:27 AMCopyright 201 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights,some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materiallyaffect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
