On R-conjugate-permutability of sylow subgroups

摘要

A subgroup H of a finite group G is said to be conjugate-permutable if HH (g) = H (g) H for all g a G. More generaly, if we limit the element g to a subgroup R of G, then we say that the subgroup H is R-conjugate-permutable. By means of the R-conjugatepermutable subgroups, we investigate the relationship between the nilpotence of G and the R-conjugate-permutability of the Sylow subgroups of A and B under the condition that G = AB, where A and B are subgroups of G. Some results known in the literature are improved and generalized in the paper.