Units OF Z(G #xD7; C2)

摘要

In this paper, we are mainly interested in describing constructivelyu(Z(G #xD7; C2)), whereu(ZG)has been described in some way. We first consider unitary units and prove that ifu(ZG)is generated by unitary units, thenU(Z(G#xD7; C2)) is also generated by unitary units. Then we consider bicyclic units and ask the following question: IfGhas a normal complement generated by bicyclic units, doesG #xD7; C2also have a normal complement generated by bicyclic units? We give a negative answer to the above in general, showing that none of the normal complements ofD8#xD7;C2#xD7;C2is generated by bicyclic units, although a normal complement ofD8#xD7;C2is indeed generated by bicyclic units.