A finite group G is said to have the nilpotent decomposition property (ND) if for every element α of integral ring Z[G] one has that αe also belong Z[G], primitive central idempotent e rational algebra Q[G]. Results Hales, Passi and Wilson, Liu Passman show this fundamental in investigations multiplicative Jordan rings. If all its subgroups ND then showed SSN, is, H, Y N G, N◁H Y⊆H N⊆Y or YN no...