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Abstrakty
The notions of permutable and globally permutable lattices were first introduced and studied by J. Krempa and B. Terlikowska-Osłowska [4]. These are lattices preserving many interesting properties of modular lattices. In this paper all finite groups with globally permutable lattices of subgroups are described. It is shown that such finite p-groups are exactly the p-groups with modular lattices of subgroups, and that the non-nilpotent groups form an essentially larger class though they have a description very similar to that of non-nilpotent modular groups.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
65-77
Opis fizyczny
Daty
wydano
1999
otrzymano
1999-02-15
poprawiono
1999-04-01
Twórcy
autor
- Institute of Mathematics, University of Białystok, Akademicka 2, 15-267 Białystok, Poland
autor
- Institute of Mathematics, University of Białystok, Akademicka 2, 15-267 Białystok, Poland
Bibliografia
- [1] G. Birkhoff, Lattice Theory, 3rd ed., Amer. Math. Soc., Providence, RI, 1967.
- [2] D. Gorenstein, Finite Simple Groups. An Introduction to Their Classification}, Plenum Press, New York, 1982.
- [3] B. Huppert, Endliche Gruppen I, Springer, Berlin, 1983.
- [4] J. Krempa and B. Terlikowska-Osłowska, On uniform dimension of lattices, in: Contributions to General Algebra 9 (Linz, 1994), Hölder-Pichler-Tempsky, Wien, 1995, 219-230.
- [5] E. Lukács, Modularity of some three-generator sublattices in subgroup lattices, Comm. Algebra 15 (1987), 2073-2080.
- [6] R. Schmidt, Subgroup Lattices of Groups, de Gruyter, Berlin, 1994.
- [7] M. Suzuki, Structure of a Group and the Structure of its Lattice of Subgroups, Springer, Berlin, 1956.
- [8] J. G. Thompson, Nonsolvable finite groups all of whose local subgroups are solvable, Bull. Amer. Math. Soc. 74 (1968), 383-434.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-cmv82i1p65bwm