# Solitary quotients of finite groups

Open Mathematics (2012)

- Volume: 10, Issue: 2, page 740-747
- ISSN: 2391-5455

## Access Full Article

top## Abstract

top## How to cite

topMarius Tărnăuceanu. "Solitary quotients of finite groups." Open Mathematics 10.2 (2012): 740-747. <http://eudml.org/doc/269796>.

@article{MariusTărnăuceanu2012,

abstract = {We introduce and study the lattice of normal subgroups of a group G that determine solitary quotients. It is closely connected to the well-known lattice of solitary subgroups of G, see [Kaplan G., Levy D., Solitary subgroups, Comm. Algebra, 2009, 37(6), 1873–1883]. A precise description of this lattice is given for some particular classes of finite groups.},

author = {Marius Tărnăuceanu},

journal = {Open Mathematics},

keywords = {Isomorphic copy; Solitary subgroups/quotients; Lattices; Chains; Subgroup lattices; Normal subgroup lattices; Dualities; solitary subgroups; solitary quotients; subgroup lattices; finite Abelian groups; lattices of normal subgroups; finite groups; isomorphism types of subgroups; normal solitary subgroups; dualities},

language = {eng},

number = {2},

pages = {740-747},

title = {Solitary quotients of finite groups},

url = {http://eudml.org/doc/269796},

volume = {10},

year = {2012},

}

TY - JOUR

AU - Marius Tărnăuceanu

TI - Solitary quotients of finite groups

JO - Open Mathematics

PY - 2012

VL - 10

IS - 2

SP - 740

EP - 747

AB - We introduce and study the lattice of normal subgroups of a group G that determine solitary quotients. It is closely connected to the well-known lattice of solitary subgroups of G, see [Kaplan G., Levy D., Solitary subgroups, Comm. Algebra, 2009, 37(6), 1873–1883]. A precise description of this lattice is given for some particular classes of finite groups.

LA - eng

KW - Isomorphic copy; Solitary subgroups/quotients; Lattices; Chains; Subgroup lattices; Normal subgroup lattices; Dualities; solitary subgroups; solitary quotients; subgroup lattices; finite Abelian groups; lattices of normal subgroups; finite groups; isomorphism types of subgroups; normal solitary subgroups; dualities

UR - http://eudml.org/doc/269796

ER -

## References

top- [1] Birkhoff G., Lattice Theory, Amer. Math. Soc. Colloq. Publ., 25, American Mathematical Society, Providence, 1967
- [2] Grätzer G., General Lattice Theory, Pure Appl. Math., 75, Academic Press, New York-London, 1978 Zbl0436.06001
- [3] Huppert B., Endliche Gruppen. I, Grundlehren Math. Wiss., 134, Springer, Berlin, 1967
- [4] Isaacs I.M., Finite Group Theory, Grad. Stud. Math., 92, Amer. American Mathematical Society, Providence, 2008 Zbl1169.20001
- [5] Kaplan G., Levy D., Solitary subgroups, Comm. Algebra, 2009, 37(6), 1873–1883 http://dx.doi.org/10.1080/00927870802116554 Zbl1176.20023
- [6] Kerby B.L., Rational Schur Rings over Abelian Groups, Master’s thesis, Brigham Young University, Provo, 2008
- [7] Kerby B.L., Rode E., Characteristic subgroups of finite abelian groups, Comm. Algebra, 2011, 39(4), 1315–1343 http://dx.doi.org/10.1080/00927871003591843 Zbl1221.20037
- [8] Schmidt R., Subgroup Lattices of Groups, de Gruyter Exp. Math., 14, de Gruyter, Berlin, 1994
- [9] Suzuki M., Structure of a Group and the Structure of its Lattice of Subgroups, Ergeb. Math. Grenzgeb., 10, Springer, Berlin-Göttingen-Heidelberg, 1956
- [10] Suzuki M., Group Theory. I, II, Grundlehren Math. Wiss., 247, 248, Springer, Berlin, 1982, 1986
- [11] Tărnăuceanu M., Groups Determined by Posets of Subgroups, Matrix Rom, Bucharest, 2006 Zbl1123.20001

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.