Brookes, C. J. B.; Smith, Howard A remark on products of locally soluble groups. (English) Zbl 0543.20024 Bull. Aust. Math. Soc. 30, 175-177 (1984). It is shown that if a group G is a product of two normal subgroups, each of which is locally soluble-of-finite-rank, then G is locally soluble if and only if it is locally of finite rank. Thus a group that is locally soluble or locally of finite rank has a unique maximal locally soluble- of-finite-rank normal subgroup. Cited in 1 Document MSC: 20F19 Generalizations of solvable and nilpotent groups 20E25 Local properties of groups 20E07 Subgroup theorems; subgroup growth 20F16 Solvable groups, supersolvable groups Keywords:product of subgroups; maximal locally soluble-of-finite-rank normal subgroup PDF BibTeX XML Cite \textit{C. J. B. Brookes} and \textit{H. Smith}, Bull. Aust. Math. Soc. 30, 175--177 (1984; Zbl 0543.20024) Full Text: DOI References: [1] Kropholler, Proc. London Math. Soc. [2] Robinson, Finiteness conditions and generalised soluble groups (1972) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.