The Margolis homology of the cohomology restriction from an extra-special group to its maximal elementary abelian subgroups

$\def\modalt{\negthickspace \negthickspace \mod \negthickspace}$Let $p$ be an odd prime and let $M_n$ be the extra-special $p$-group of order $p^{2n+1} \; (n \geqslant 1)$ and exponent $p^2$. We completely compute the $\modalt p$ Margolis homology of the image $\mathrm{ImRes} (A, M_n)$ for every maximal elementary abelian $p$-subgroup $A$ of $M_n$.

Keywords

Steenrod algebra, Milnor operation, Margolis homology, invariant theory, Dickson–Mùi algebra

2010 Mathematics Subject Classification

55N99, 55S05, 55S10

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Dedicated to Professor Nguyễn H. V. Hưng on the occasion of his 70th birthday.

Received 29 November 2022

Accepted 13 March 2023

Published 20 March 2024