Finite groups with globally permutable lattice of subgroups

• Autorzy: C. Bagiński , A. Sakowicz
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1999
• Tom: 82
• Numer: 1
• Strony: 65-77

Daty

wydano

1999

otrzymano

1999-02-15

poprawiono

1999-04-01

Twórcy

autor

C. Bagiński

• Institute of Mathematics, University of Białystok, Akademicka 2, 15-267 Białystok, Poland

autor

A. Sakowicz

• 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.