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Topic: How to show a group is a subgroup of A_14?
Replies: 1   Last Post: Dec 21, 2007 11:13 AM

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tianran.chen@gmail.com

Posts: 49
Registered: 6/3/05
How to show a group is a subgroup of A_14?
Posted: Dec 21, 2007 10:25 AM
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Greetings,

Problem: I want to show that a simple group G of order 4*3*7*13 must
be isomorphic to a subgroup of A_14 (the alternating group of 14
letters).

Attempt: It is easy to show that there are 14 sylow 13-subgroups. And
so G act by conjugation on its sylow 7-subgroups with a trivial kernel
(since G is simple). This shows that G is a subgroup of S_14 (the
symmetric group of 14 letters). What's the next step? Thanks in
advance.



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