Omegas of agemos in powerful groups

James L I Williams

doi:10.22108/ijgt.2019.113217.1507

Omegas of agemos in powerful groups

James L I Williams

School of Mathematics

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

Abstract

Let G be a powerful p-group. In this note we investigate when the Omega subgroups of the Agemo subgroups of G are Powerfully Nilpotent. We discuss the difference between the cases when p=2 and when p is an odd prime. Moreover this work gives an example of a characteristic subgroup of G^{p} which is Powerfully Nilpotent but not strongly powerful.

Original language	English
Journal	International Journal of Group Theory
Early online date	13 Mar 2019
DOIs	https://doi.org/10.22108/ijgt.2019.113217.1507
Publication status	E-pub ahead of print - 13 Mar 2019

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10.22108/ijgt.2019.113217.1507

https://arxiv.org/abs/1811.00977

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abstract = "Let G be a powerful p-group. In this note we investigate when the Omega subgroups of the Agemo subgroups of G are Powerfully Nilpotent. We discuss the difference between the cases when p=2 and when p is an odd prime. Moreover this work gives an example of a characteristic subgroup of G^{p} which is Powerfully Nilpotent but not strongly powerful.",

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AB - Let G be a powerful p-group. In this note we investigate when the Omega subgroups of the Agemo subgroups of G are Powerfully Nilpotent. We discuss the difference between the cases when p=2 and when p is an odd prime. Moreover this work gives an example of a characteristic subgroup of G^{p} which is Powerfully Nilpotent but not strongly powerful.

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DO - 10.22108/ijgt.2019.113217.1507

M3 - Article (Academic Journal)

JO - International Journal of Group Theory

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