P-localizing group extensions with a finite kernel

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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
Volume139
Issue number2
DOIs
StatePublished - Sep 1 2005

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Group Extension
P-groups
kernel
Nilpotent Group
Exact Sequence
Free Group
Functor
Class

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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 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.",
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P-localizing group extensions with a finite kernel. / Lorensen, Karl.

In: Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 139, No. 2, 01.09.2005, p. 193-206.

Research output: Contribution to journalArticle

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