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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.

 
 
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