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On nilpotent and polycyclic groups

Published online by Cambridge University Press:  17 April 2009

Robert J. Hursey
Robert J. Hursey
Affiliation:
East Carolina UniversityGreenville NC 27834United States of America
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Abstract

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A group G is torsion-free, finitely generated, and nilpotent if and only if G is a supersolvable R-group. An ordered polycylic group G is nilpotent if and only if there exists an order on G with respect to which the number of convex subgroups is one more than the length of G. If the factors of the upper central series of a torsion-free nilpotent group G are locally cyclic, then consecutive terms of the series are jumps, and the terms are absolutely convex subgroups.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 40 , Issue 1 , August 1989 , pp. 119 - 122
Copyright
Copyright © Australian Mathematical Society 1989

References

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