Leader: Prof. Dr. Ákos Pintér, full professor
The group-theoretical properties of the group of units and its unitary subgroups in group ring and in crossed algebra. Description of involutions in group rings and the study of corresponding unitary subgroups of the group of units. Determination of the generating system of the group of units and its unitary subgroups. Computation of the nilpotency class and the exponent of the group of units and its unitary subgroups in modular algebra. The Lie properties of the group algebra and crossed products. Application of Lie properties for studying the group of units in group algebra. Determination of formal languages and codes possessing special algebraic, combinatorial and algorithmic properties. Description of composition of automata and sequential machines by means of group algebraic methods.