On generalized plus-constructions of Eilenberg–Mac Lane spaces

A GEM is an infinite loop space which is weakly equivalent to a product of Eilenberg–Mac Lane spaces. In this paper, the fiber of any f-localization map of a GEM is shown to be a GEM again. Using this result, we compute explicitly the p-local and p-torsion generalized plus-constructions of abelian Eilenberg–Mac Lane spaces. We also prove some arithmetic square results to compute the generalized plus-construction of Eilenberg–Mac Lane spaces in general.