An example of an element of the inverse limit that is not an element of " G " is an infinite commutator.
12.
However " G " is not the complete inverse limit but rather the subgroup in which each generator appears only finitely many times.
13.
In addition one can define Serre groups of algebraic number fields, and the Serre group is the inverse limit of the Serre groups of number fields.
14.
The name " Mittag-Leffler " for this condition was given by Bourbaki in their chapter on uniform structures for a similar result about inverse limits of complete Hausdorff uniform spaces.
15.
That is, the next element of the sequence equals the last, modulo one more power of " p "; this gives the projection defining the inverse limit.
16.
:I would take as a definition that Z _ p is the inverse limit of Z / p ^ nZ ( i . e ., formal power series in p ).
17.
That is, the automorphisms of F fixing " F " are described by the inverse limit, as we take larger and larger finite splitting fields over " F ".
18.
An interesting fact is that the pure braid group in this group is isomorphic to both the inverse limit of finite pure braid groups and to the fundamental group of the Hilbert cube minus the set
19.
First, every compact group ( understood to be Hausdorff ) is an inverse limit of compact Lie groups . ( One important case is an inverse limit of finite groups, called a profinite group.
20.
First, every compact group ( understood to be Hausdorff ) is an inverse limit of compact Lie groups . ( One important case is an inverse limit of finite groups, called a profinite group.
