Modulo odd prime homotopy normality for $H$-spaces

Abstract

Given an $H$-map $i : Y \to X$, we say that $i$ is mod $p$ homotopy normal if the commutator map from $X_{(p)}\times Y_{(9)}$ to $X_{(p)}$ can be deformed into $Y_{(p)}$. In this paper, we study necessary conditions of mod $p$ homotopy normality for the cases that $X$ are exceptional Lie groups with odd torsion in the cohomology, by using the Morava K-theory.