Right exact localizations of groups

We introduce several classes of localizations (idempotent monads) on the category groups and study their properties relations. The most interesting class for us is which coincide with zero derived functors. call them right exact (in sense Keune). prove that a localization L preserves nilpotent finite p-group G map → LG an epimorphism. also some examples (Baumslag’s P-localization respect to set primes P, Bousfield’s H R-localization, Levine’s localization, Levine-Cha’s ℤ-localization) are exact. At end paper we discuss conjecture Farjoun about Nikolov-Segal maps very special case this conjecture.