P-localizing group extensions with a nilpotent action on the kernel

Research output: Contribution to journalArticle

Abstract

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
Volume34
Issue number12
DOIs
StatePublished - Dec 1 2006

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Group Extension
Nilpotent Group
P-groups
kernel
Functor
Injection
Generalise
Family

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

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abstract = "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 NP → lP 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.",
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P-localizing group extensions with a nilpotent action on the kernel. / Lorensen, Karl.

In: Communications in Algebra, Vol. 34, No. 12, 01.12.2006, p. 4345-4364.

Research output: Contribution to journalArticle

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