  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 p-compact 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 p-compact 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 operations.
