Pro-resolvable group

In mathematics, more precisely in algebra , a group is called pro-solvable if it is isomorphic to the inverse limit of an inverse system of solvable groups. A pro-resolvable group is a special case of a Pro-C group .

Examples

• Let p be a prime number . If we denote the field of the p-adic numbers with as usual , then the Galois group , where denotes the algebraic closure of , is pro-resolvable. ${\displaystyle \mathbf {Q} _{p}}$ ${\displaystyle {\text{Gal}}\left({\overline {\mathbf {Q} }}_{p}/\mathbf {Q} _{p}\right)}$ ${\displaystyle {\overline {\mathbf {Q} }}_{p}}$ ${\displaystyle \mathbf {Q} _{p}}$

See also

• Profinite group

Individual evidence

1. ^ Nigel Boston: The Proof of Fermat's Last Theorem. University of Wisconsin, Madison WI 2003, digitized version (PDF; 586.41 kB) .