Prosolvable group
Appearance
In
open neighborhood of the identity contains a normal subgroup whose corresponding quotient group
is a solvable group.
Examples
- Let p be a p-adic numbers, as usual, by . Then the Galois group , where denotes the algebraic closure of , is prosolvable. This follows from the fact that, for any finite Galois extension of , the Galois group can be written as semidirect product , with cyclic of order for some , cyclic of order dividing , and of -power order. Therefore, is solvable.[1]
See also
References
- ^ Boston, Nigel (2003), The Proof of Fermat's Last Theorem (PDF), Madison, Wisconsin, USA: University of Wisconsin Press