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Automorphisms of nilpotent groups of class two with small rank

Part of: Structure and classification of infinite or finite groups Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

Thomas A. Fournelle
Thomas A. Fournelle
Affiliation:
Science DivisionUniversity of Wisconsin-ParksideKenosha, Wisconsin 53141, U.S.A.
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Abstract

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Rational abelian groups, that is, torsion-free abelian groups of rank one, are characterized by their types. This paper characterizes rational nilpotent groups of class two, that is, nilpotent groups of class two in which the center and central factor group are direct sums of rational abelian groups. This characterization is done according to the types of the summands of the center and the central factor group. Using these types and some cohomological techniques it is possible to determine the automorphism group of the nilpotent group in question by performing essentially matrix computations.

In particular, the automorphism groups of rational nilpotent groups of class two and rank three are completely described. Specific examples are given of semicomplete and pseudocomplete nilpotent groups.

MSC classification

Secondary: 20F28: Automorphism groups of groups 20F18: Nilpotent groups 20E36: Automorphisms of infinite groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 39 , Issue 1 , August 1985 , pp. 121 - 131
Copyright
Copyright © Australian Mathematical Society 1985

References

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