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Converse of a theorem of Mal’cev on nilpotent groups. (English) Zbl 0276.20027


MSC:

20E15 Chains and lattices of subgroups, subnormal subgroups
20D15 Finite nilpotent groups, \(p\)-groups
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References:

[1] Hall, P.: Some sufficient conditions for a group to be nilpotent, Illinois J. Math.2, 787-801 (1958) · Zbl 0084.25602
[2] Huppert, B.: Endliche Gruppen I. Berlin-Heidelberg-New York: Springer 1967 · Zbl 0217.07201
[3] Kostrikin, A.I.: On Burnside’s problem, Izvestija Akad. Nauk SSSR, Ser. mat.23, 3-34 (1959) · Zbl 0090.24503
[4] Lennox, J.C.: A note on a centrality property of finitely generated soluble groups, Proc. Cambridge philos. Soc.75, 23-24 (1974) · Zbl 0273.20022 · doi:10.1017/S0305004100048180
[5] Mal’cev, A.I.: Homomorphisms onto finite groups, Ivanov. Gos. Ped. Inst. U?en. Zap. Fiz.-Mat. Nauki8, 49-60 (1958)
[6] Novikov, P.S., Adjan, P.S.: Infinite periodic groups I, II, III, Izvestija Akad. Nauk SSSR, Ser. mat.32, 209-236, 241-479, 665-685 (1968) · Zbl 0194.03301 · doi:10.1070/IM1968v002n01ABEH000637
[7] Robinson, D.J.S.: A theorem on finitely generated hyperabelian groups, Inventiones Math.10, 38-43 (1970) · Zbl 0198.34504 · doi:10.1007/BF01402969
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