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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Classification of metabelian $ p$-groups


Author: Wu Nan Chou
Journal: Trans. Amer. Math. Soc. 294 (1986), 151-176
MSC: Primary 20D15; Secondary 20F12
DOI: https://doi.org/10.1090/S0002-9947-1986-0819940-1
MathSciNet review: 819940
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Abstract: Let $ G$ be a two-generator metabelian group of exponent $ p$ with class of nilpotence $ c$, where $ c \leqslant p - 1$ and $ p$ is an odd prime. In this paper, we shall consider the classification problem when $ \vert{G_2}/{G_3}\vert = p$, $ \vert{G_3}/{G_4}\vert = {p^2}$and $ \vert{G_4}/{G_5}\vert \leqslant {p^2}$.


References [Enhancements On Off] (What's this?)

  • [1] B. Huppert, Endliche Gruppen. I, Die Grundlehren der Math. Wissenchaften, Band 134, Springer-Verlag, Berlin and New York. MR 0224703 (37:302)
  • [2] R. Miech, The metabelian $ p$-groups of maximal class, Trans. Amer. Math. Soc. 236 (1978), 93-119. MR 0486126 (58:5912)
  • [3] -, A metabelian, prime power classification problem, J. London Math. Soc. (2) 23 (1981), 68-84. MR 602240 (82j:20047)
  • [4] -, A commutator basis, Quart. J. Math. Oxford Ser. (2) 135 (1983), 357. MR 711526 (85b:20027)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1986-0819940-1
Keywords: $ p$-groups, metabelian groups
Article copyright: © Copyright 1986 American Mathematical Society

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