P-localizing group extensions with a finite kernel

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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 languageEnglish (US)
Pages (from-to)193-206
Number of pages14
JournalMathematical Proceedings of the Cambridge Philosophical Society
Issue number2
StatePublished - Sep 1 2005

All Science Journal Classification (ASJC) codes

  • General Mathematics


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