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On groups with a triple factorisation

Published online by Cambridge University Press:  20 January 2009

Andrew Fransman
Andrew Fransman
Affiliation:
Department of Mathematics and Applied Mathematics, University of the Western Cape, Private Bag X17, 7535 Bellville, South Africa. E-mail address: [email protected]
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Abstract

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The aim of this paper is to discuss groups G=HK=HA=KA with a triple factorisation as a product of two subgroups H and K and a nilpotent normal subgroup A. It is of interest to know whether such a group G satisfies some nilpotency or supersolubility condition if H and K satisfy the same condition. A positive answer to this problem is given for certain group classes under the hypothesis that A is prefactorised in G = HK. Some applications of the main theorem are also mentioned.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 38 , Issue 3 , October 1995 , pp. 421 - 429
Copyright
Copyright © Edinburgh Mathematical Society 1995

References

REFERENCES

1.Amberg, B., Artinian and noetherian factorized groups, Rend. Sem. Mat. Univ. Padov. 55 (1976), 105–122.Google Scholar
2.Amberg, B., Triply factorized groups, in Groups St Andrews 1989 Volume I (Campbell, C. M. and Robertson, E. F., eds.), (London Math. Soc. Lecture Notes Series 159, CUP Cambridge, New York, Port Chester, Melbourne, Sydney, 1991), pp. 1–13.Google Scholar
3.Amberg, B., Franciosi, S. and De Giovanni, F., Groups with an FC-nilpotent triple factorization, Ricerche Mat. 36 (1987), 103–114.Google Scholar
4.Amberg, B., Franciosi, S. and De Giovanni, F., Groups with a nilpotent triple factorisation, Bull. Austral. Math. Soc. 37 (1988), 69–79.Google Scholar
5.Amberg, B., Franciosi, S. and De Giovanni, F., Groups with a supersoluble triple factorization, J. Algebra 117 (1988), 136–148.Google Scholar
6.Amberg, B., Franciosi, S. and De Giovanni, F., FC-nilpotent products of hypercentral groups, to appear.Google Scholar
7.Amberg, B., Franciosi, S. and De Giovanni, F., Products of groups (Clarendon Press, Oxford, 1992).Google Scholar
8.Amberg, B. and Fransman, A., Products of groups and group classes, Israel J. Math. 87 (1994), 9–18.Google Scholar
9.Amberg, B. and Hofling, B., On finite products of nilpotent groups, Arch. Math. 63 (1994), 1–8.Google Scholar
10.Amberg, B. and Robinson, D. J. S., Soluble groups which are products of nilpotent minimax groups, Arch. Math. 42 (1984), 385–390.CrossRefGoogle Scholar
11.Fransman, A., Factorizations of groups (Ph.D Thesis, Univ. of Amsterdam, The Netherlands, 1991).Google Scholar
12.Kegel, O. H., Zur Struktur mehrfach faktorisierter endlicher Gruppen, Math. Z. 87 (1965), 42–48.Google Scholar
13.Mclain, D. H., Remarks on the upper central series of a group, Proc. Glasgow Math. Assoc. 3 (1956), 38–44.Google Scholar
14.Pennington, E., On products of finite nilpotent groups, Math. Z. 134 (1973), 81–83.Google Scholar
15.Robinson, D. J. S., On the theory of subnormal subgroups, Math. Z. 89 (1965), 30–51.Google Scholar
16.Robinson, D. J. S., A property of the lower central series of a group, Math Z. 107 (1968), 225–231.CrossRefGoogle Scholar
17.Robinson, D. J. S., Finiteness conditions and generalized soluble groups (Springer-Verlag, Berlin, Heidelberg, New York, 1972).Google Scholar
18.Robinson, D. J. S., A course in the theory of groups (Springer-Verlag, New York, Heidelberg, Berlin, 1982).Google Scholar
19.Sysak, Y. P., Products of infinite groups (preprint 82.53), Akad. Nauk. Ukr. Mat. Kiev (1982), 1–36.Google Scholar
20.Wielandt, H., Über Produkte vomiilpotenten Gruppen, Illinois J. Math. 2 (1958), 611–618.Google Scholar