Normalizer of Sylow p-subgroup of simple groups A_n

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Discussion Overview

The discussion revolves around the order of the normalizer of Sylow p-subgroups in the simple groups A_n. Participants explore the challenges associated with computing this order and its implications for counting Sylow p-subgroups.

Discussion Character

  • Technical explanation, Debate/contested

Main Points Raised

  • One participant questions the difficulty of counting the Sylow p-subgroups of A_n.
  • Another participant asserts that while computing the order of Sylow p-subgroups is straightforward, determining the order of their normalizer is complex.
  • A different participant suggests that computing the order of the normalizer could facilitate counting the number of Sylow p-subgroups, but acknowledges that this task is generally considered very difficult.

Areas of Agreement / Disagreement

Participants express differing views on the complexity of the problems involved, with no consensus on the overall difficulty of computing the normalizer's order or the implications for counting Sylow p-subgroups.

Contextual Notes

Participants do not specify assumptions or definitions that may affect their claims, and the discussion does not resolve the mathematical steps involved in these computations.

rulin
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what is the order of normalizer of Sylow p-subgroup of simple groups A_n?
 
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So you basically want to count the Sylow p-subgroups of A_n. Isn't this a very hard problem?
 
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?
 
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 anyone of them in the group), which is (as far as I know) very difficult.
 

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