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Groups with a nilpotent triple factorisation

Published online by Cambridge University Press:  17 April 2009

Bernhard Amberg ,
Silvana Franciosi  and
Francesco de Giovanni
Bernhard Amberg
Affiliation:
Fachbereich Mathematik, Universität Mainz, Saarstraße 21, D-6500 Mainz, West Germany.
Silvana Franciosi
Affiliation:
Dipartimento di Matematica, Università di Napoli, via Mezzocannone 8, I - 80134 Napoli, Italy.
Francesco de Giovanni
Affiliation:
Dipartimento di Matematica, Università di Napoli, via Mezzocannone 8, I - 80134 Napoli, Italy.
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Abstract

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In the investigation of factorised groups one often encounters groups G = AB = AK = BK which have a triple factorisation as a product of two subgroups A and B and a normal subgroup K of G. It is of particular interest to know whether G satisfies some nilpotency requirement whenever the three subgroups A, B and K satisfy this same nilpotency requirement. A positive answer to this problem for the classes of nilpotent, hypercentral and locally nilpotent groups is given under the hypothesis that K is a minimax group or G has finite abelian section rank. The results become false if K has only finite Prüfer rank. Some applications of the main theorems are pointed out.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 37 , Issue 1 , February 1988 , pp. 69 - 79
Copyright
Copyright © Australian Mathematical Society 1988

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