On a class of lattice subgroup functors.
type: Item
instance of: scholarly article
title: On a class of lattice subgroup functors.
zbMATH Open document ID: 1253.20010
DOI: 10.1134/S0001434611030059
published in: Mathematical Notes
publication date: 2011-11-25T00:00:00Z
review text: From the summary: ``In the paper, continuum-many natural transitive lattice subgroup functors corresponding to no hereditary lattice formation are constructed on the class of all finite groups. This result is an answer to Question 15.39 in `The Kourovka notebook', which was posed by the author and A. F. Vasil'ev in connection with their theorem claiming that, on the class of all solvable groups, all functors of this kind correspond to hereditary local lattice formations.'' The lattice subgroup functors in question interpolate between the \(\mathfrak F\)-subnormal subgroups and Kegel \(\mathfrak F\)-subnormal subgroups, both with respect to a hereditary lattice formation \(\mathfrak F\).
reviewed by: Russ Woodroofe
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D30
Mathematics Subject Classification ID: 20D35
zbMATH DE Number: 5980780
zbMATH Keywords: lattices of subgroups
zbMATH Keywords: hereditary lattice formations
zbMATH Keywords: natural transitive lattice semigroup functors
zbMATH Keywords: finite solvable groups
zbMATH Keywords: subgroup functors
zbMATH Keywords: NLT functors
author: S. F. Kamornikov
MaRDI profile type: Publication
cites work: Eine Verallgemeinerung der invarianten Untergruppen
cites work: Subgroup lattices of finite groups which properly contain the lattice of subnormal subgroups
cites work: Q3961010
cites work: Q4344341
cites work: On the lattice of \(\mathcal F\)-subnormal subgroups
cites work: On the functorial method for studying the lattices of subgroups of finite groups
cites work: Finite soluble groups
cites work: The \(\mathfrak F\)-normalizers of a finite soluble group
cites work: Über den Normalisator der subnormalen Untergruppen
cites work: Q3031177
full work available at URL: s0001434611030059
OpenAlex ID: W2053901048
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description: scientific article; zbMATH DE number 5980780