Infinite loop spaces from group theory (Q1365452)

The paper considers factorizations of the Hurewicz map from stable homotopy to singular homology by homology theories arising from symmetric monoidal categories defined by compatible choices of families of subgroups of the symmetric groups. The main example studied comes from the elementary abelian \(p\)-subgroups generated by disjoint cycles. The homotopy type of the corresponding infinite loop space becomes calculated (after completion). The method is to relate \(h\)-pushouts of connective spectra with two-sided bar-constructions on infinite loop spaces. Further analysis of the two-sided bar-construction then makes use of [\textit{J. P. May}, Classifying spaces and fibrations; Mem. Am. Math. Soc. 155 (1975; Zbl 0321.55033)].