Normal subgroups of powerful p-groups

James L I Williams

Normal subgroups of powerful p-groups

James L I Williams

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

Abstract

In this note we show that if p is an odd prime and G is a powerful p-group with N≤G^{p} and N normal in G, then N is powerfully nilpotent. An analogous result is proved for p=2 when N≤G^{4}.

Original language	English
Journal	Israel Journal of Mathematics
Publication status	Accepted/In press - 12 Sep 2019

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https://arxiv.org/abs/1908.07030

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title = "Normal subgroups of powerful p-groups",

abstract = "In this note we show that if p is an odd prime and G is a powerful p-group with N≤G^{p} and N normal in G, then N is powerfully nilpotent. An analogous result is proved for p=2 when N≤G^{4}.",

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year = "2019",

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day = "12",

language = "English",

journal = "Israel Journal of Mathematics",

issn = "0021-2172",

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T1 - Normal subgroups of powerful p-groups

AU - Williams, James L I

PY - 2019/9/12

Y1 - 2019/9/12

N2 - In this note we show that if p is an odd prime and G is a powerful p-group with N≤G^{p} and N normal in G, then N is powerfully nilpotent. An analogous result is proved for p=2 when N≤G^{4}.

AB - In this note we show that if p is an odd prime and G is a powerful p-group with N≤G^{p} and N normal in G, then N is powerfully nilpotent. An analogous result is proved for p=2 when N≤G^{4}.

M3 - Article (Academic Journal)

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

SN - 0021-2172

ER -

Normal subgroups of powerful p-groups

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