Brandl, Rolf; Franciosi, Silvana; de Giovanni, Francesco On the Wielandt subgroup of infinite soluble groups. (English) Zbl 0726.20023 Glasg. Math. J. 32, No. 2, 121-125 (1990). Denote by \(\omega\) (G) the Wielandt subgroup of a group G, that is the intersection of the normalizers of all subnormal subgroups of G. The authors have two main results. If G is finitely generated soluble-by- finite with finite Prüfer rank then \(\omega\) (G) is contained in the FC-centre of G. Also if G is a polycyclic group which is either (a) metanilpotent or (b) abelian-by-finite, then \(\omega\) (G)/Z(G) is finite. There are examples showing the limits of the results. Reviewer: J.D.P.Meldrum (Edinburgh) Cited in 7 Documents MSC: 20F16 Solvable groups, supersolvable groups 20E07 Subgroup theorems; subgroup growth 20E15 Chains and lattices of subgroups, subnormal subgroups Keywords:Wielandt subgroup; normalizers; subnormal subgroups; finitely generated soluble-by-finite; finite Prüfer rank; FC-centre; polycyclic group; metanilpotent; abelian-by-finite PDFBibTeX XMLCite \textit{R. Brandl} et al., Glasg. Math. J. 32, No. 2, 121--125 (1990; Zbl 0726.20023) Full Text: DOI References: [1] DOI: 10.1112/plms/s3-9.4.595 · Zbl 0091.02501 · doi:10.1112/plms/s3-9.4.595 [2] Cossey, Australian National University, Math. 19 (1988) [3] DOI: 10.1007/BF01110066 · Zbl 0169.33801 · doi:10.1007/BF01110066 [4] Baer, Compositio Math. 1 pp 254– (1934) [5] DOI: 10.1017/S0305004100037403 · doi:10.1017/S0305004100037403 [6] DOI: 10.1007/BF01187422 · Zbl 0082.24703 · doi:10.1007/BF01187422 [7] Robinson, Finiteness conditions and generalized soluble groups (1972) · doi:10.1007/978-3-662-07241-7 [8] Robinson, Compositio Math. 21 pp 240– (1969) [9] DOI: 10.1007/BF01111712 · Zbl 0134.26004 · doi:10.1007/BF01111712 [10] DOI: 10.1016/0021-8693(64)90029-8 · Zbl 0121.03002 · doi:10.1016/0021-8693(64)90029-8 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.