A note on finite metabelian 𝑝-groups

Gillam, J. D.

doi:10.1090/S0002-9939-1970-0254132-2

Proceedings of the American Mathematical Society

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A note on finite metabelian $p$-groups
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by J. D. Gillam

Proc. Amer. Math. Soc. 25 (1970), 189-190

DOI: https://doi.org/10.1090/S0002-9939-1970-0254132-2

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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 $A$.

References

J. L. Alperin, Large Abelian subgroups of $p$-groups, Trans. Amer. Math. Soc. 117 (1965), 10–20. MR 170946, DOI 10.1090/S0002-9947-1965-0170946-4
Daniel Gorenstein, Finite groups, Harper & Row, Publishers, New York-London, 1968. MR 0231903