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Transactions of the American Mathematical Society

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



Abelian subgroups of finite $ p$-groups

Author: Susan Claire Dancs
Journal: Trans. Amer. Math. Soc. 169 (1972), 489-493
MSC: Primary 20D15
MathSciNet review: 0308258
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Abstract: Information is obtained about the order of maximal abelian subgroups of central powers and crown products of finite $ p$-groups. This is used to construct groups with ``small'' maximal abelian subgroups.

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

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  • [2] B. Huppen, Endliche Gruppen. I, Die Grundlehren der math. Wissenschaften, Band 134, Springer-Verlag, Berlin and New York, 1967. MR 37 #302. MR 0224703 (37:302)
  • [3] G. A. Miller, On the number of abelian subgroups whose order is a power of a prime, Messenger Math. 36 (1906/07), 79-80.
  • [4] B. H. Neumann, Ascending derived series, Composttio Math. 13 (1956), 47-64; Corrigendum, ibid., p. 128. MR 19, 632. MR 0089196 (19:632b)

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Keywords: Abelian subgroups, finite $ p$-group, central power, crown product
Article copyright: © Copyright 1972 American Mathematical Society

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