In this note we show that for any powerful $p$-group $G$, the subgroup $\Omega_{i}(G^{p^{j}})$ is powerfully nilpotent for all $i,j\geq1$ when $p$ is an odd prime, and $i\geq1$, $j\geq2$ when $p=2$. We provide an example to show why this modification is needed in the case $p=2$. Furthermore we obtain a bound on the powerful nilpotency class of $\Omega_{i}(G^{p^{j}})$.
Williams, J. (2020). Omegas of agemos in powerful groups. International Journal of Group Theory, 9(3), 185-192. doi: 10.22108/ijgt.2019.113217.1507
MLA
James Williams. "Omegas of agemos in powerful groups". International Journal of Group Theory, 9, 3, 2020, 185-192. doi: 10.22108/ijgt.2019.113217.1507
HARVARD
Williams, J. (2020). 'Omegas of agemos in powerful groups', International Journal of Group Theory, 9(3), pp. 185-192. doi: 10.22108/ijgt.2019.113217.1507
VANCOUVER
Williams, J. Omegas of agemos in powerful groups. International Journal of Group Theory, 2020; 9(3): 185-192. doi: 10.22108/ijgt.2019.113217.1507
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