Abstract
In the case where a group G is a productG=AB of Abelian subgroupsA andB one of which has a finite 0-rank, we prove that the Fitting subgroupF and the Hirsch-Plotkin radicalR admit the decompositionsF=(F∩ A)(F ∩ B) andR=(R∩A)(R ∩ B), respectively. This gives the affirmative answer to one question of B. Amberg.
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References
N. Itô, “Über das Produkt von zwei abelschen Gruppen,”Math. Z.,62, No. 3 400–401 (1955).
B. Amberg, “Products of two Abelian subgroups,”Rocky Mount. J. Math.,14, No. 3, 541–547 (1984).
Ya. P. Sysak,Products of Infinite Groups [in Russian], Preprint 82.53, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1982).
B. Amberg, “Infinite factorized groups,”Springer Lect. Notes Math.,1398, 1–24 (1988).
D. J. S. Robinson,A Course in the Theory of Groups, Springer, Berlin (1982).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 457–461, April, 1994.
This paper was supported by the Ukrainian State Foundation on Science and Technology.
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Sysak, Y.P. On one question of B. Amberg. Ukr Math J 46, 488–491 (1994). https://doi.org/10.1007/BF01060423
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DOI: https://doi.org/10.1007/BF01060423