normalizer of Sylow p-subgroup of simple groups A_n


by rulin
Tags: groups, normalizer, psubgroup, simple, sylow
rulin
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#1
Sep20-08, 09:48 PM
P: 7
what is the order of normalizer of Sylow p-subgroup of simple groups A_n?
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morphism
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#2
Sep21-08, 02:16 AM
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So you basically want to count the Sylow p-subgroups of A_n. Isn't this a very hard problem?
rulin
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#3
Sep21-08, 05:11 AM
P: 7
the order of sylow p-subgroup of A_n is not hard to compute, but the one of normalizer of sylow p-subgroup, how to compute?

morphism
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#4
Sep21-08, 06:31 PM
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normalizer of Sylow p-subgroup of simple groups A_n


But my point is if you compute the order of the normalizer of an arbitrary Sylow p-subgroup, then you can count the number of Sylow p-subgroups (because the number of Sylows is the index of the normalizer of any one of them in the group), which is (as far as I know) very difficult.


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