We have “triangle” “rectangle” “pentagon”…etc “tetrahedral” “cube” “octahedron” …etc
Instead of having to say “group” all the time, like “dihedral group” “cyclic group”, if we make it into one word it will sound more like an elementary mathematical object.
What would be a nice suffix for group?
What about, following Forum and Quorum, “-um” (or “-rum”).
Trirum; Tetrum; Octum; Dihedrum; Cyclicum;
Not sure on Abelian. Abelium? That works.