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On Normal Subgroups of Products of Nilpotent Groups

Part of: Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

Bernhard Amberg ,
Silvana Franciosi  and
Francesco De Giovanni
Bernhard Amberg
Affiliation:
Fachbereich Mathematik Universität MainzSaarstrasse 21 D-6500 Mainz West, Germany
Silvana Franciosi
Affiliation:
Fachbereich Mathematik Universität MainzSaarstrasse 21 D-6500 Mainz West, Germany
Francesco De Giovanni
Affiliation:
Dipartimento di Matematica Università di Napoli Via Mezzocannone8 1-80134 Napoli, Italy
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Abstract

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Let G be a group factorized by finitely many pairwise permutable nilpotent subgroups. The aim of this paper is to find conditions under which at least one of the factors is contained in a proper normal subgroup of G.

MSC classification

Secondary: 20F16: Solvable groups, supersolvable groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 44 , Issue 2 , April 1988 , pp. 275 - 286
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Amberg, B., ‘Über auflösbare Produkte nilpotenter Gruppen’, Arch. Math. (Basel) 30 (1978), 361–363.CrossRefGoogle Scholar
[2]Amberg, B., ‘Products of two abelian subgroups’, Rocky Mountain J. Math. 14 (1984), 541–547.CrossRefGoogle Scholar
[3]Amberg, B., ‘Produkte von Gruppen mit endlichem torsionfreiem Rang’, Arch. Math. (Basel) 45 (1985), 398–406.Google Scholar
[4]Amberg, B., ‘On groups which are the product of abelian subgroups’, Glasgow Math. J. 26 (1985), 151–156.Google Scholar
[5]Amberg, B. and Robinson, D. J. S., ‘Soluble groups which are products of nilpotent minimax groups’, Arch. Math. (Basel) 42 (1984), 385–390.Google Scholar
[6]Belyaev, V. V., ‘Locally finite groups with Černikov Sylow p-subgroups’, Algebra i Logika 20 (1981), 605–619 =Google Scholar
Algebra and Logic 20 (1981), 393–402.CrossRefGoogle Scholar
[7]Černikov, N. S., ‘Factorable locally graded groups’, Dokl. Akad. Nauk SSSR 260 (1981), 543–546 =Google Scholar
Soviet Math. Dokl. 24 (1981), 312–315.Google Scholar
[8]Gillam, H. D., ‘A finite p-group P = AB with Core (A) = Core (B) = 1’, Rocky Mountain J. Math. 3 (1973), 15–17.Google Scholar
[9]Holt, D. F. and Howlett, R. B., ‘On groups which are the product of two abelian groups’, J. London Math. Soc. (2) 29 (1984), 453–461.CrossRefGoogle Scholar
[10]Itô, N., ‘Über das Produkt von zwei abelschen Gruppen’, Math. Z. 62 (1955), 400–401.Google Scholar
[11]Kegel, O. H., ‘Produkte nilpotenter Gruppen’, Arch. Math. (Basel) 12 (1961), 90–93.Google Scholar
[12]Kegel, O. H. and Wehrfritz, B. A. F., Locally finite groups (North-Holland, Amsterdam, 1973).Google Scholar
[13]Miedniak, B., ‘Auflösbare Produkte unendlicher Gruppen’ (Diplomarbeit, Mainz, 1985).Google Scholar
[14]Robinson, D. J. S., ‘A property of the lower central series of a group’, Math. Z. 107 (1968), 225–231.CrossRefGoogle Scholar
[15]Robinson, D. J. S., Finiteness conditions and generalized soluble groups, Part 1 and 2 (Springer, Berlin, 1972).CrossRefGoogle Scholar
[16]Robinson, D. J. S., ‘Soluble products of nilpotent groups’, J. Algebra 98 (1986), 183–196.CrossRefGoogle Scholar
[17]Wehrfritz, B. A. F., Infinite linear groups (Springer, Berlin, 1973).CrossRefGoogle Scholar
[18]Wielandt, H., ‘Über Produkte von nilpotenten Gruppen’, Illinois J. Math. 2 (1958), 611–618.Google Scholar
[19]Zaičev, D. I., ‘Products of abelian groups’, Algebra i Logika 19 (1980), 150–172 =Google Scholar
Algebra and Logic 19 (1980), 94–106.CrossRefGoogle Scholar