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

Full Text (PDF format)

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