Solitary quotients of finite groups

• Autorzy: Marius Tărnăuceanu
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Isomorphic copy; Solitary subgroups/quotients; Lattices; Chains; Subgroup lattices; Normal subgroup lattices; Dualities

Kategorie tematyczne

• 20D15: Nilpotent groups, p -groups
• 20D30: Series and lattices of subgroups
• 20D99: None of the above, but in this section
• 20D40: Products of subgroups

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 2
• Strony: 740-747

Daty

wydano

2012-04-01

online

2012-01-18

Twórcy

autor

Marius Tărnăuceanu

• “Al.I. Cuza” University

Bibliografia

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• [5] Kaplan G., Levy D., Solitary subgroups, Comm. Algebra, 2009, 37(6), 1873–1883 http://dx.doi.org/10.1080/00927870802116554
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• [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
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• [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

Identyfikatory

DOI

10.2478/s11533-012-0003-0