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T-groups, polycyclic groups, and finite quotients

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Abstract

A group is called a T-group if all of its subnormal subgroups are normal. In this note we consider the following question: Assume that G is a polycyclic group. What can be said about G if all finite epimorphic images H of G satisfy one of the following conditions: (i) H is a T-group,(ii) \({H/\Phi (H)}\) is a T-group,(iii) H/Z *(H) is a T-group. We will see that the prime 2 will play a particular role in (ii) and (iii), see Theorems C and D.

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Authors and Affiliations

  1. Institut fuer Mathematik, Universitaet Wuerzburg, Wuerzburg, Germany

    Hermann Heineken

  2. Department of Mathematics, University of Kentucky, Lexington, KY, USA

    James C. Beidleman

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  1. Hermann Heineken
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  2. James C. Beidleman
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Correspondence to Hermann Heineken.

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Dedicated to Otto H. Kegel on the occasion of his eightieth birthday.

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Heineken, H., Beidleman, J.C. T-groups, polycyclic groups, and finite quotients. Arch. Math. 103, 21–26 (2014). https://doi.org/10.1007/s00013-014-0670-0

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