GAPlus(1,R) is rationally powered
This article gives the statement, and possibly proof, of a particular group or type of group (namely, GAPlus(1,R) (?)) satisfying a particular group property (namely, Rationally powered group (?)).
The group , denoted GAPlus(1,R), defined explicitly as the group under composition of maps from to of the form:
is a rationally powered group. In other words, for any positive integer and any element , there is a unique such that .
Suppose is the map:
We want to find all elements that are maps of the form such that . By composing with itself times, we get
For this to equal , we know that the coefficient of and the constant term should match up separately, so we get:
Solving, we get that the unique solution is the element with:
In other words, the solution is: