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Topic: Let G be a group , N a normal subgroup of G
Replies: 13   Last Post: Feb 6, 2013 6:11 AM

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Ken.Pledger@vuw.ac.nz

Posts: 1,380
Registered: 12/3/04
Re: Let G be a group , N a normal subgroup of G
Posted: Feb 5, 2013 3:46 PM
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In article
<692dbadf-ec9e-40cf-a2a3-9348d0aedad7@fv9g2000vbb.googlegroups.com>,
Dan <dan.ms.chaos@gmail.com> wrote:

> Does there always exist a subgroup H of G such that G = NH , and
> (H intersection N) = the identity element?



You've had the general answer "no", but the situation you describe is
quite significant. Such a group G is called a "split extension" or a
"semi-direct product". You may like to look up those terms.

Ken Pledger.



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