16S34 16U60 6 20C05 5 20C07 5 group ring 5 group algebra 4 integral group ring 4 unit group 4 20N15 3 11B85 2 17B30 2 20C05; 20D08 2 20E08 2 94B15 2 94B60 2 Kaplansky conjecture 2 Kimmerle conjecture 2 Lie dimension subgroups 2 Lie nilpotency index 2 Thue-Morse sequence 2 Zassenhaus conjecture 2 commutative 2 dihedral group 2 direct product 2 group algebras 2 group code 2 group rings 2 idempotent 2 minimal code 2 partial augmentation 2