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Regular metabelian groups of prime-power order

Published online by Cambridge University Press:  17 April 2009

R. J. Faudree
R. J. Faudree
Affiliation:
University of Illinois at Urbana-Champaign, Urbana, Illinois, USA.
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Abstract

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Let H be a finite metabelian p-group which is nilpotent of class c. In this paper we will prove that for any prime p > 2 there exists a finite metacyclic p-group G which is nilpotent of class c such that H is isomorphic to a section of a finite direct product of G.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 3 , Issue 1 , August 1970 , pp. 49 - 54
Copyright
Copyright © Australian Mathematical Society 1970

References

[1] Hall, P., “On a theorem of Frobenius”, Proc. London Math. Soc. (2) 40 (1936), 468–501.CrossRefGoogle Scholar
[2] Hall, P., “A note on -groups”, J. London Math. Soc. 39 (1964), 338–344CrossRefGoogle Scholar
[3] Higman, Graham, “Some remarks on varieties of groups”, Quart. J. Math. Oxford Ser. (2) 10 (1959), 165–178.CrossRefGoogle Scholar
[4] Macdonald, I.D., “The variety of regular p-groups”, Arch. Math. 18 (1967), 359–361.CrossRefGoogle Scholar
[5] Weichsel, Paul M., “Regular p-groups and varieties”, Math. Z. 95 (1967), 223–231.CrossRefGoogle Scholar
[6] Weichsel, Paul M., “On metabelian p-groups”, J. Austral. Math. Soc. 7 (1967), 55–63.CrossRefGoogle Scholar