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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




Re: Yes
Posted:
Feb 5, 2013 11:34 AM


Dan <dan.ms.chaos@gmail.com> wrote in news:43bcf4320c9a41e29eea 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 counterexample. I'm surprised you aren't more grateful.
B.



