group [a,b,c] -- makes a free ordered commutative group on the variables listed.
group [a,b,c,Degrees=>{2,3,4}] -- makes a free ordered commutative group on the variables listed, with degrees 2, 3, and 4, respectively.
group [a,b,c,Degrees=>{{1,2},{3,-3},{0,4}}] -- makes a free ordered commutative group on the variables listed, with multi-degrees as listed.
group [a,b,c,Degrees=>{{},{},{}}] -- makes a free ordered commutative group on the variables listed, ungraded.
The class of all groups created this way is GeneralOrderedMonoid.
See also Degrees, OrderedMonoid, and monoid.