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Topic: Subgroups and conjugates
Replies: 4   Last Post: Dec 1, 2012 4:08 PM

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Michael Klemm

Posts: 117
Registered: 11/13/12
Re: Subgroups and conjugates
Posted: Dec 1, 2012 12:49 PM
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"Carsten Schultz" <schultz@zedat.fu-berlin.de> wrote in message
news:ahutbaFu3lqU1@mid.uni-berlin.de...
> On 01.12.12 16:56, Jacques Willekens wrote:
>> Is it possible for an infinite subgroup to be conjugate to
>> one of its porper subgroups ?
>>

>
> Yes, the following should work: In the free group on generators a and b
> let H be the subgroup generated by all a^n b a^{-n}, n>=0. Then aHa^{-1}
> is a proper subgroup of H.


One should distinguish between conjugacy by an element of the free group G
and conjugacy by an element by an element of H.

Regards
Michael





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