Some Results Of The Population Center Of The Ring And Symmetrical Units

Research on group rings has always been an important direction of group algebra. Based on the results of previous studies, we make further discussion about the center of group rings and symmetric elements in group rings, related results on several aspects are obtained which we state as follows:Let G+be the set of symmetric elements of group G, and (FG)+be the set of symmetric elements of FG. At first, assume (FG)+be the ring, we discuss the relationship between (FG)+and the center of group ring ξ(FG), We know that if G isn’t an Abel group,(FG)+is a ring. If charF≠2, then we can get the conclusion (FG)+=ξ(FG). Next, we discuss the relationship of symmetric units between group ring and factor group ring, so under certain conditions, we have the epimorphism relationship of symmetric units between FG and F(G/N) is proved...