Monoids on the 2-disk (Q788117)

D is a monoid on the 2-disk. The following are proved in this paper: 1. A compact group can act as a group of units of a monoid D on 2-disk if and only if it can be represented as an Abelian subgroup of the group 0(2) of 2\(\times 2\) orthogonal matrices. 2. Any compact group of monoid automorphisms of D is effectively isomorphic to the two element group. 3. The centralizer of any compact of units of D and also the fixed point set of any compact group of monoid automorphisms of D are connected.