P-localizing group extensions with a nilpotent action on the 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 a group extension giving rise to a nilpotent action of G on N, we prove that the sequence NPlP GP∈P QP → 1 is exact. Moreover, in the case where Q satisfies a certain pair of homological conditions, we show that the map ιP is an injection. This generalizes the well-known result that ()P is exact in the category of nilpotent groups. Applications are given to calculating P-localizations of virtually nilpotent groups.

Original languageEnglish (US)
Pages (from-to)4345-4364
Number of pages20
JournalCommunications in Algebra
Issue number12
StatePublished - Dec 1 2006

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


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