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You are not logged in. #1 20090425 07:16:54
The Jordan–Hölder theoremI am now reading about this in Chapter 15 of A Course in Group Theory by John E. Humphreys. Last edited by JaneFairfax (20090425 07:17:43) #2 20090427 02:38:53
Re: The Jordan–Hölder theoremThe Zassenhaus lemma is merely a result about normal subgroups. The way to prove this is to prove that and that the LHS is isomorphic to ; it will follow by symmetry that the RHS is also isomorphic to this group and hence to the LHS. According to Wikipedia, this result is also called the butterfly lemma. There is a lovely picture of a butterfly on the Wikipedia article as well. 