Assume P is a family of primes, and let ()P represent the P-localization functor. If 1 → N →L G, → ∈ Q → 1 is an exact sequence of groups with N finite, we prove that the sequence NPLP GP →∈P QP→ 1 is exact. Moreover, we provide an explicit description of KeriP when Q belongs to a specific class of groups defined by a cohomological property. This class contains all nilpotent groups, all free groups and all P-local groups, as well as certain extensions formed from these three types of groups. In conclusion, we discuss the implications of our results for the study of finite-by-nilpotent groups.
|Original language||English (US)|
|Number of pages||14|
|Journal||Mathematical Proceedings of the Cambridge Philosophical Society|
|State||Published - Sep 1 2005|
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