Dual-standard subgroups in nonperiodic locally soluble groups

Stewart E. Stonehewer; Giovanni Zacher

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1990)

  • Volume: 1, Issue: 2, page 101-104
  • ISSN: 1120-6330

Abstract

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Let G be a non-periodic locally solvable group. A characterization is given of the subgroups-D of G for which the map X → X ∩ D , for all X ≤ G , defines a lattice-endomorphism.

How to cite

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Stonehewer, Stewart E., and Zacher, Giovanni. "Dual-standard subgroups in nonperiodic locally soluble groups." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 1.2 (1990): 101-104. <http://eudml.org/doc/244189>.

@article{Stonehewer1990,
abstract = {Let G be a non-periodic locally solvable group. A characterization is given of the subgroups-D of G for which the map \( X \to X \cap D \), for all \( X \leq G \), defines a lattice-endomorphism.},
author = {Stonehewer, Stewart E., Zacher, Giovanni},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Group; Lattice; Lattice-endomorphism; dual-standard subgroups; non-periodic locally soluble groups},
language = {eng},
month = {5},
number = {2},
pages = {101-104},
publisher = {Accademia Nazionale dei Lincei},
title = {Dual-standard subgroups in nonperiodic locally soluble groups},
url = {http://eudml.org/doc/244189},
volume = {1},
year = {1990},
}

TY - JOUR
AU - Stonehewer, Stewart E.
AU - Zacher, Giovanni
TI - Dual-standard subgroups in nonperiodic locally soluble groups
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1990/5//
PB - Accademia Nazionale dei Lincei
VL - 1
IS - 2
SP - 101
EP - 104
AB - Let G be a non-periodic locally solvable group. A characterization is given of the subgroups-D of G for which the map \( X \to X \cap D \), for all \( X \leq G \), defines a lattice-endomorphism.
LA - eng
KW - Group; Lattice; Lattice-endomorphism; dual-standard subgroups; non-periodic locally soluble groups
UR - http://eudml.org/doc/244189
ER -

References

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  1. IVANOV, S. G., L-homomorphisms of locally solvable torsion-free groups. Mat. Zametki, 37, 1985, 627-635. Zbl0584.20019MR797702
  2. IVANOV, S. G., Standard and dually standard elements of the subgroup lattice of a group. Algebra i Logika, 8, 1969, 440-446. Zbl0266.20033MR280601
  3. STONEHEWER, S. E. - ZACHER, G., Lattice homomorphisms of non-periodic groups. J. Algebra, to appear. Zbl0741.20019MR1102568DOI10.1016/0021-8693(91)90191-A
  4. STONEHEWER, S. E. - ZACHER, G., Lattice homomorphisms of groups and dual standard subgroups. Springer Lecture Notes in Mathematics, to appear. Zbl0704.20025MR1068369
  5. STONEHEWER, S. E. - ZACHER, G., Dual-standard subgroups of finite and locally finite groups, to appear. Zbl0728.20026MR1085626DOI10.1007/BF02568364
  6. SUZUKI, M., Structure of a group and the structure of its lattice of subgroups. Springer Verlag, 1967. Zbl0070.25406MR83487
  7. ZAPPA, G., Sulla condizione perché un emitropismo inferiore tipico tra due gruppi sia un omotropismo. Giornale di Mat. Battaglini, 80, 1951, 80-101. Zbl0043.02501MR41139

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