1 $Z_3$-graded 1 17A05,17A30 1 17B40 1 18A32 1 20C05,16L30 1 20D10 1 Church thesis 1 Lie algebra 1 Primary 20L05; Secondary 20N02 1 Serial ring 1 UDC 681.3 1 \(\pi\)-length,nilpotent \(\pi\)-length 1 \(\pi\)-solvable group 1 \(p\) -length 1 \(p\)-rank 1 \(p\)-solvable group 1 alternative algebra 1 bicyclic group 1 commutative 1 derivation 1 derived length 1 direct product 1 group ring 1 groupoid 1 metacyclic group 1 nilalgebra 1 nilpotent ideal 1 nilpotent lengths 1 rank 1