On the number of diamonds in the subgroup lattice of a finite abelian group

Dan Gregorian Fodor; Marius Tărnăuceanu

doi:10.1515/auom-2016-0037

.blurhash-client-img { display: none !important; }

On the number of diamonds in the subgroup lattice of a finite abelian group

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 24 (2016): Issue 2 (June 2016)

By: Dan Gregorian Fodor and Marius Tărnăuceanu

Open Access

|Sep 2017

Abstract

The main goal of the current paper is to determine the total number of diamonds in the subgroup lattice of a finite abelian group. This counting problem is reduced to finite p-groups. Explicit formulas are obtained in some particular cases.

References

[1] Bidwell, J.N.S., Curran, M.J., McCaughan, D.J., Automorphisms of di- rect products of finite groups, Arch. Math. 86 (2006), 481-489.10.1007/s00013-005-1547-z
Search in Google Scholar Back to article
[2] Birkhoff, G., Subgroups of abelian groups, Proc. Lond. Math. Soc. 38 (1934, 1935), 385-401.10.1112/plms/s2-38.1.385
Search in Google Scholar Back to article
[3] Birkhoff, G., Lattice theory, Amer. Math. Soc., Providence, R.I., 1967.
Search in Google Scholar Back to article
[4] Grätzer, G., General lattice theory, Academic Press, New York, 1978.10.1007/978-3-0348-7633-9
Search in Google Scholar Back to article
[5] Hillar, C.J., Rhea, D.L., Automorphisms of finite abelian groups, Amer. Math. Monthly 114 (2007), 917-923.10.1080/00029890.2007.11920485
Search in Google Scholar Back to article
[6] Isaacs, I.M., Finite group theory, Amer. Math. Soc., Providence, R.I., 2008.10.1090/gsm/092
Search in Google Scholar Back to article
[7] Schmidt, R., Subgroup lattices of groups, de Gruyter Expositions in Mathematics 14, de Gruyter, Berlin, 1994.
Search in Google Scholar Back to article
[8] Schmidt, R., L-free groups, Illinois J. Math. 47 (2003), 515-528.10.1215/ijm/1258488169
Search in Google Scholar Back to article
[9] Schmidt, R., L10-free groups, J. Group Theory 10 (2007), 613-631.10.1515/JGT.2007.046
Search in Google Scholar Back to article
[10] Suzuki, M., Group theory, I, II, Springer Verlag, Berlin, 1982, 1986.10.1007/978-3-642-86885-6
Search in Google Scholar Back to article
[11] Suzuki, M., Structure of a group and the structure of its lattice of sub- groups, Ergebnisse der Mathematik und ihrer Grenzgebiete, Neue Folge, Heft 10, Springer Verlag, Berlin-Göttingen-Heidelberg, 1956.
Search in Google Scholar Back to article
[12] Tărnăuceanu, M., Groups determined by posets of subgroups, Ed. Matrix Rom, Bucureşti, 2006.
Search in Google Scholar Back to article
[13] Tărnăuceanu, M., A new method of proving some classical theorems of abelian groups, Southeast Asian Bull. Math. 31 (2007), 1191-1203.
Search in Google Scholar Back to article
[14] Tărnăuceanu, M., An arithmetic method of counting the subgroups of a finite abelian group, Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 53/101 (2010), 373-386.
Search in Google Scholar Back to article
[15] Tărnăuceanu, M., A characterization of the quaternion group, Sci. An. Univ. “Ovidius“ Constanţa 21 (2013), 209-214.10.2478/auom-2013-0013
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.1515/auom-2016-0037 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

Journal RSS Feed

Language: English

Page range: 205 - 215

Submitted on: Feb 9, 2015

Accepted on: Mar 2, 2015

Published on: Sep 21, 2017

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

section,

Related subjects:

© 2017 Dan Gregorian Fodor, Marius Tărnăuceanu, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 24 (2016): Issue 2 (June 2016)