March 21st, 2009, 10:00 AM  #1 
Newbie Joined: Mar 2009 Posts: 21 Thanks: 0  Double Cosets
Let and be subgroups of the group . For each define the double coset of in to be the set . a) Prove that is the union of the left cosets where is the orbit containing of acting by left multiplication on the set of left cosets of . b) Prove that is a union of right cosets of . c) Show that and are either the same set or are disjoint for all . Show that the set of double cosets partitions . d) Prove that . e) Prove that . This is, well, exercise 4.1.10 from Dummit & Foote. It doesn't seem too difficult, but for some reason, I can't seem to do it. Independent studies are quite frustrating at times. Sigh. 

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cosets, double 
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