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

Abstract

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 $\mod p$ Margolis homology of the image ImRes $(A, M_n)$ for every maximal elementary abelian $p$-subgroup $A$ of $M_n$.