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Presentations of metacyclic groups

Published online by Cambridge University Press:  17 April 2009

Bruce W. King
Affiliation:
School of Applied Sciences, Riverina College of Advanced Education, Wagga Wagga, New South Wales.
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Abstract

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Each metacyclic p–group has a natural canonical presentation which is easily derived from the usual presentation. Parameters in the canonical presentation measure how far the group is from splitting, and from being either commutative or dihedral. The structure of the groups is discussed.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Basmaji, B.G., “On the isomorphisms of two. metacyclic groups”, Proc. Amer. Math. Soc. 22 (1969), 175182.Google Scholar
[2]Beyl, F. Rudolf, “The classification of metacyclic p-groups”, Notices Amer. Math. Soc. 19 (1972), 696–20–9.Google Scholar
[3]Burnside, W.. Theory of groups of finite order, 2nd ed. (Cambridge University Press, Cambridge, 1911; reprinted, Dover, New York, 1955).Google Scholar
[4]Huppert, B., Endliche Gruppen I (Die Grundlehren der mathematischen Wissenschaften, Band 134. Springer-Verlag, Berlin, Heidelberg, New York, 1967).CrossRefGoogle Scholar
[5]Lindenberg, Wolfgang, “Über die Struktur zerfallender bizyklischer p-Gruppen”, J. reine angew. Math. 241 (1970), 118146.Google Scholar
[6]Lindenberg, Wolfgang, “Über die Struktur zerfallender nicht-modularer bizyklischer 2-Gruppen”, Ber. Ges. Math. Datenverarbeitung, Bonn 29 (1970), 163.Google Scholar
[7]Lindenberg, Wolfgang, “Struktur und Klassifizierung bizyklischer p-Gruppen”, Ber. Ges. Math. Datenverarbeitung, Bonn 40 (1971), 136.Google Scholar
[8]Passman, D.S., “Nonnormal subgroups of p-groups”, J. Algebra 15 (1970), 352370.CrossRefGoogle Scholar