Adjective
nonabelian (not comparable)
Not abelian.
Hence it is surprising that Tarski's student Wanda Szmielew (1955) proved that the first order theory of abelian groups, unlike its nonabelian counterpart, is decidable. Source: Internet
However, matrix multiplication is not commutative, therefore this group is nonabelian. Source: Internet
The classification of nonabelian simple groups is far less trivial. Source: Internet