The nilpotence height of 𝑃_{𝑡}^{𝑠}

Monks, Kenneth

doi:10.1090/S0002-9939-96-03150-4

The nilpotence height of $P_t^s$
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by Kenneth G. Monks

Proc. Amer. Math. Soc. 124 (1996), 1297-1303

DOI: https://doi.org/10.1090/S0002-9939-96-03150-4

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Abstract:

The method of Walker and Wood is used to completely determine the nilpotence height of the elements $P_t^s$ in the Steenrod algebra at the prime 2. In particular, it is shown that $(P_t^s)^{2\lfloor s/t \rfloor +2}=0$ for all $s\ge 0$, $t\ge 1$. In addition, several interesting relations in $A$ are developed in order to carry out the proof.

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