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 Posted: Sun Jul 13, 2008 6:54 am Post subject: Set products and groups |
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If H, K are two subgroups in G then we can consider the product HK
that could not be a group. Instead, if one of those groups is normal,
then HK is a subgroup of G.
Suppose one of them is normal. When H and K have only the identity of
G in common, is HK the semidirect product of H and K? |
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Tonico
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| Posted: Sun Jul 13, 2008 7:26 am Post subject: Re: Set products and groups |
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On Jul 13, 9:54 am, blee...@gmail.com wrote:
| Quote: |
If H, K are two subgroups in G then we can consider the product HK
that could not be a group. Instead, if one of those groups is normal,
then HK is a subgroup of G.
Suppose one of them is normal. When H and K have only the identity of
G in common, is HK the semidirect product of H and K?
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Yes. That's precisely the definition of semidirect product: if H is
normal, take the homom. K --> Aut(H) determined by conjugation by K
to form the semidirect product.
Regards
Tonio |
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