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 Post subject: Recognizing SubgroupsPosted: Sun, 19 Feb 2012 02:29:27 UTC
 S.O.S. Oldtimer

Joined: Sat, 21 Jan 2012 03:59:22 UTC
Posts: 182

Im working on #2. Just a quick question which may turn out to be more complicated, but on showing the inverse is in H
'log(n^-1)' if n is an integer is n inverse (n^-1) also an integer? i know log(n^-1) wont always be an integer but 'n' inverse would be, wouldn't it?

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 Post subject: Re: Recognizing SubgroupsPosted: Sun, 19 Feb 2012 02:42:56 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
DgrayMan wrote:

Im working on #2. Just a quick question which may turn out to be more complicated, but on showing the inverse is in H
'log(n^-1)' if n is an integer is n inverse (n^-1) also an integer? i know log(n^-1) wont always be an integer but 'n' inverse would be, wouldn't it?

The elements of are real numbers such that for some . Now, since the original, underlying group is we need to consider and as is is true that is also a positive integer, and the answer should be obvious: not unless , so fails to be a subgroup of .

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 Post subject: Re: Recognizing SubgroupsPosted: Sun, 19 Feb 2012 03:15:41 UTC
 S.O.S. Oldtimer

Joined: Sat, 21 Jan 2012 03:59:22 UTC
Posts: 182
haden't thought of using e. thanks

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 Post subject: Re: Recognizing SubgroupsPosted: Sun, 19 Feb 2012 03:19:19 UTC
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DgrayMan wrote:
haden't thought of using e. thanks

You don't have to, you can directly just know that if then ergo and since was a positive integer, in order for it must be that , but of course we can pick the x with and its inverse is missing.

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