Groups of unstable Adams operations on p-local compact groups

A p-local compact group is an algebraic object modelled on the homotopy theory associated with p-completed classifying spaces of compact Lie groups and pcompact groups. In particular p-local compact groups give a unified framework in which one may study p-completed classifying spaces from an algebraic and
homotopy theoretic point of view. Like connected compact Lie groups and pcompact groups, p-local compact groups admit unstable Adams operations - self equivalences that are characterised by their cohomological effect. Unstable Adams operations on p-local compact groups were constructed in a previous paper by F. Junod and the authors. In the current paper we study groups of unstable operations from a geometric and algebraic point of view. We give a precise description of the relationship between algebraic and geometric operations, and show that under some conditions unstable Adams operations are determined by their degree. We also examine a particularly well behaved subgroup of unstable Adams operations.