Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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.
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
740-747
Opis fizyczny
Daty
wydano
2012-04-01
online
2012-01-18
Twórcy
Bibliografia
- [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
- [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
- [5] Kaplan G., Levy D., Solitary subgroups, Comm. Algebra, 2009, 37(6), 1873–1883 http://dx.doi.org/10.1080/00927870802116554
- [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
- [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
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-012-0003-0