Hostname: page-component-76fb5796d-9pm4c Total loading time: 0 Render date: 2024-04-26T16:32:25.382Z Has data issue: false hasContentIssue false
  • English
  • Français

On Finite Groups with Dismantlable Subgroup Lattices

Published online by Cambridge University Press:  20 November 2018

Marius Tărnăuceanu
Marius Tărnăuceanu*
Affiliation:
Faculty of Mathematics, “Al.I. Cuza” University, Iaşi, Romania. e-mail: tarnauc@uaic.ro
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this note we study the finite groups whose subgroup lattices are dismantlable.

Keywords

20D3020D6020E15finite groupssubgroup latticesdismantlable latticesplanar latticescrowns
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 58 , Issue 1 , 01 March 2015 , pp. 182 - 187
Copyright
Copyright © Canadian Mathematical Society 2015

References

[1] Baker, K.A., Fishburn, P.C., Roberts, F.S., Partial orders of dimension z, interval orders, and interval graphs, Rand Corp. P-4376 (1970).Google Scholar
[2] Birkhoff, G., Lattice theory. Third ed., American Mathematical Society Colloquium Publications, American Mathematical Society, Providence, R.I., 1967.Google Scholar
[3] Grätzer, G., General lattice theory. Pure and Applied Mathematics, 6þ, Academic Press, New York-London, 1978.Google Scholar
[4] Isaacs, I. M., Finite group theory. Graduate Studies in Mathematics, 92, Americna Mathematical Society, Providence, RI, 2008.Google Scholar
[5] Kelly, D. and Rival, I., Crowns, fences, and dismantlable lattices. Canad. J. Math. 26 (1974), 1257. http://dx.doi.org/10.4153/CJM-1974-120-2 Google Scholar
[6] Rival, I., Lattices with doubly irreducible elements. Canad. Math. Bull. 17(1974),. 1257–1271 http://dx.doi.org/10.4153/CMB-1974-016-3 Google Scholar
[7] Schmidt, R., Subgroup lattices of groups. de Gruyter Expositions in Mathematics, 14, Walter de Gruyter, Berlin, 1994.Google Scholar
[8] Schmidt, R., Planar subgroup lattices. Algebra Universalis, 55 (2006), no. 1, 3–12 Google Scholar
[9] Suzuki, M., Structure of a group and the structure of its lattice of subgroups. Ergebnisse der Mathematik und ihrer Grenzgebiete, Neue Folge, Heft, 10, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1956.Google Scholar
[10] Suzuki, M., Group theory. I Grundlehren der Mathematischen Wissenschaften, 248, Springer-Verlag, Berlin-New York, 1982, II. Grundlehren der Mathematischen Wissenschaften, 248, Springer-Verlag, New York, 1986.Google Scholar
[11] Tărnăuceanu, M., Groups determined by posets of subgroups. Matrix Rom, Bucharest, 2006Google Scholar