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You are not logged in. #1 20080628 09:39:51#2 20081009 09:10:55
Re: Group theoryIndeed, this is a rather cool result. In fact, it generalizes fairly well. That is, if G contains a subgroup H of index p for the smallest prime dividing the order of G, then H is normal in G. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #3 20090328 21:37:40
Re: Group theoryThe first mathematician to use the term “group” was Évariste Galois (according to the book A Course in Group Theory by John F. Humphreys). At about that same time, Augustin Louis Cauchy was independently studying these mathematical structures, but it was Galois’s terminology which became universally adopted. Last edited by JaneFairfax (20090415 03:12:59) #4 20090402 00:01:45#5 20090402 00:31:34
Re: Group theoryLast edited by JaneFairfax (20090402 05:52:31) #6 20090402 00:35:42#7 20090407 10:18:33#8 20090409 02:42:23#9 20090411 00:20:28#10 20090411 00:32:19#11 20090413 00:27:06
Re: Group theory
I’ve just read it A Course in Group Theory by John F. Humphreys! It is stated as Corollary 9.25 on page 86. states that there is a normal subgroup with and . In fact, is the kernel of a homomorphism mapping to the permutation group of the set of all left cosets of in . I have read every proof in my book carefully, and have followed every proof so far. I can thus safely say that I haven’t missed any trick, big or small. Last edited by JaneFairfax (20090415 03:13:17) 