Proceedings of the Japan Academy, Series A, Mathematical Sciences

On products of cyclic and abelian finite $p$-groups ($ p$ odd)

Brendan McCann

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Abstract

For an odd prime $p$, it is shown that if $G = AB$ is a finite $p$-group, for subgroups $A$ and $B$ such that $A$ is cyclic and $B$ is abelian of exponent at most $p^{k}$, then $\Omega_{k}(A)B \unlhd G$, where $\Omega_{k}(A) = \langle g \in A \mid g^{ p^{k}} = 1 \rangle$.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 94, Number 8 (2018), 77-80.

Dates
First available in Project Euclid: 29 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.pja/1538186760

Digital Object Identifier
doi:10.3792/pjaa.94.77

Mathematical Reviews number (MathSciNet)
MR3859763

Subjects
Primary: 20D40: Products of subgroups 20D15: Nilpotent groups, $p$-groups

Keywords
Products of groups factorised groups finite $p$-groups

Citation

McCann, Brendan. On products of cyclic and abelian finite $p$-groups ($ p$ odd). Proc. Japan Acad. Ser. A Math. Sci. 94 (2018), no. 8, 77--80. doi:10.3792/pjaa.94.77. https://projecteuclid.org/euclid.pja/1538186760


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References

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