Prosolvable group
In mathematics, more precisely in algebra, a prosolvable group (less common: prosoluble group) is a group that is isomorphic to the inverse limit of an inverse system of solvable groups. Equivalently, a group is called prosolvable, if, viewed as a topological group, every open neighborhood of the identity contains a normal subgroup whose corresponding quotient group is a solvable group.
01Examples
- Let p be a prime, and denote the field of p-adic numbers, as usual, by
. Then the Galois group
, where
denotes the algebraic closure of
of
can be written as semidirect product
, with
cyclic of order
for some
,
cyclic of order dividing
, and
of
-power order. Therefore,
Sources and credits
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