Proof, or a sketch thereof.
There exists a regular tree on which acts, with stabilizer (here, denotes the ring of -adic integers (http://planetmath.org/PAdicIntegers)). Since is compact in its profinite topology, so is . Thus, must be compact, discrete and torsion-free. Since compact and discrete implies finite, the only such group is trivial. Thus, acts freely on . Since groups acting freely on trees are free, is free. ∎
|Date of creation||2013-03-22 13:54:26|
|Last modified on||2013-03-22 13:54:26|
|Last modified by||bwebste (988)|