The main result in the paper states the following: For a finite group , which is the product of the soluble subgroups and , if is a metanilpotent group for all and , then the factor groups are nilpotent, denoting the Fitting subgroup of . A particular generalization of this result and some consequences are also obtained. For instance, such a group is proved to be soluble of nilpotent length at most , assuming that the factors and have nilpotent length at most . Also for any finite soluble group and , an element is contained in the preimage of the hypercenter of , where denotes the ()th term of the Fitting series of , if and only if the subgroups have nilpotent length at most for all .
Cite this article
M. Pilar Gállego, Peter Hauck, M. Dolores Pérez-Ramos, Soluble products of connected subgroups. Rev. Mat. Iberoam. 24 (2008), no. 2, pp. 433–461DOI 10.4171/RMI/542