A note on finite metabelian $p$-groups
Author:
J. D. Gillam
Journal:
Proc. Amer. Math. Soc. 25 (1970), 189-190
MSC:
Primary 20.25
DOI:
https://doi.org/10.1090/S0002-9939-1970-0254132-2
MathSciNet review:
0254132
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Abstract: Let $A$ be an abelian subgroup of maximal order in the finite metabelian $p$-group $P$. It is shown that there exists a normal abelian subgroup ${A_1}$ of $P$ such that the order of ${A_1}$ is equal to the order of $A$.
- J. L. Alperin, Large Abelian subgroups of $p$-groups, Trans. Amer. Math. Soc. 117 (1965), 10–20. MR 170946, DOI https://doi.org/10.1090/S0002-9947-1965-0170946-4
- Daniel Gorenstein, Finite groups, Harper & Row, Publishers, New York-London, 1968. MR 0231903
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Keywords:
Metabelian <IMG WIDTH="16" HEIGHT="37" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="$p$">-group,
abelian subgroup of maximal order
Article copyright:
© Copyright 1970
American Mathematical Society