Cohomology of loop spaces of the symmetric space \(EI\) (Q1947741)

In the paper under review, the author determines the mod \(p\) cohomology of the loop space and the double loop space of the symmetric space of exceptional type \(EI\). The cohomology of \(EI\) was determined by \textit{K. Ishitoya} [Proc. Japan Acad., Ser. A 53, 56--60 (1977; Zbl 0395.57029)] and \textit{K. Ishitoya} and \textit{H. Toda} [J. Math. Kyoto Univ. 17, 225-243 (1977; Zbl 0366.57012)], who proved that it has two torsion, but no odd torsions. The present author uses the Serre spectral sequence and the Eilenberg-Moore spectral sequence to calculate the cohomology. Then it is shown that the cohomology of the loop space of \(EI\) has only two torsion.