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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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 Bart Goddard Posts: 1,707 Registered: 12/6/04
Re: Yes
Posted: Feb 5, 2013 11:34 AM
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Dan <dan.ms.chaos@gmail.com> wrote in news:43bcf432-0c9a-41e2-9eea-
c91fe4e809ee@ia3g2000vbb.googlegroups.com:

> On Feb 5, 4:24 pm, Robin Chapman <R.J.Chap...@ex.ac.uk> wrote:
>> On 05/02/2013 14:08, Dan wrote:
>>
>>
>>
>>
>>
>>
>>

>> > On Feb 5, 3:45 pm, Robin Chapman <R.J.Chap...@ex.ac.uk> wrote:
>> >> On 05/02/2013 13:27, Dan wrote:
>>
>> >>> Does there always exist a subgroup H of G such that G = NH  , and
>> >>> (H intersection N) = the identity element?

>>
>> > Can you provide an example?
>
> Fun fact :If the set of possible answers is infinite , and person T (T
> stands for troll) claims to have one ,then person B cannot determine
> for sure using only yes or no questions . Each question is a function
> from the set of remaining answers to {Yes,No} . Provided that the set
> is infinite , either the inverse image to Yes or the inverse image of
> No is infinite . There exists a sequence of choices as answers of T
> such that the set of 'remaining valid answers' always remains
> infinite , thereby always giving the impression of knowledge of an
> answer , while ensuring for a fact that such an answer does not
> exist .

That's an interesting alternative universe you've got there. Something
closer to reality would be that person T (T for teacher) doesn't want to
do your homework for you, but was helpful enough to tell you the right
answer, so that you wouldn't waste a lot of time looking for a proof
rather than a counter-example. I'm surprised you aren't more grateful.

B.

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