A simple proof of Baer;s and Sato's theorems on lattice-isomorphisms between groups

Mario Mainardis

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1992)

  • Volume: 3, Issue: 3, page 173-176
  • ISSN: 1120-6330

Abstract

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A simple proof is given of a well-known result of the existance of lattice-isomorphisms between locally nilpotent quaternionfree modular groups and abelian groups.

How to cite

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Mainardis, Mario. "A simple proof of Baer;s and Sato's theorems on lattice-isomorphisms between groups." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 3.3 (1992): 173-176. <http://eudml.org/doc/244219>.

@article{Mainardis1992,
abstract = {A simple proof is given of a well-known result of the existance of lattice-isomorphisms between locally nilpotent quaternionfree modular groups and abelian groups.},
author = {Mainardis, Mario},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Group; Lattice; Lattice-isomorphism; quasinormal subgroups; isomorphic lattices of subgroups; -groups; abelian group},
language = {eng},
month = {9},
number = {3},
pages = {173-176},
publisher = {Accademia Nazionale dei Lincei},
title = {A simple proof of Baer;s and Sato's theorems on lattice-isomorphisms between groups},
url = {http://eudml.org/doc/244219},
volume = {3},
year = {1992},
}

TY - JOUR
AU - Mainardis, Mario
TI - A simple proof of Baer;s and Sato's theorems on lattice-isomorphisms between groups
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1992/9//
PB - Accademia Nazionale dei Lincei
VL - 3
IS - 3
SP - 173
EP - 176
AB - A simple proof is given of a well-known result of the existance of lattice-isomorphisms between locally nilpotent quaternionfree modular groups and abelian groups.
LA - eng
KW - Group; Lattice; Lattice-isomorphism; quasinormal subgroups; isomorphic lattices of subgroups; -groups; abelian group
UR - http://eudml.org/doc/244219
ER -

References

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  1. BAER, R., Crossed isomorphisms. Amer. J. of Math., 66, 1944, 341-404. Zbl0061.03601MR10589
  2. IWASAWA, K., Über die endlichen Gruppen und die Verbände ihrer Untergruppen. Journal of Univ. of Tokyo, 4-3, 1941, 171-199. Zbl0061.02503MR5721
  3. IWASAWA, K., On the structure of infinite M-groups. Jap. Journal of Math., 18, 1943, 709-728. Zbl0061.02504MR15118
  4. MAINARDIS, M., Projektivitäten zwischen abelschen und nichtabehchen Gruppen. Arch. Math., 57, 1991, 332-338. Zbl0723.20015MR1124494DOI10.1007/BF01198956
  5. POLAND, J., On verifying lattice-isomorphisms of a group. Arch. Math., 44, 1985, 309-310. Zbl0545.20017MR788942DOI10.1007/BF01235771
  6. SATO, S., Note on lattice-isomorphisms between abelian groups and non abelian groups. Osaka Math. J., 3, 1951, 215-220. Zbl0044.01104MR45113

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