# Finite groups with globally permutable lattice of subgroups

Colloquium Mathematicae (1999)

- Volume: 82, Issue: 1, page 65-77
- ISSN: 0010-1354

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topBagiński, C., and Sakowicz, A.. "Finite groups with globally permutable lattice of subgroups." Colloquium Mathematicae 82.1 (1999): 65-77. <http://eudml.org/doc/210751>.

@article{Bagiński1999,

abstract = {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.},

author = {Bagiński, C., Sakowicz, A.},

journal = {Colloquium Mathematicae},

keywords = {subgroup lattices; finite modular lattices; globally permutable lattices; finite groups; modular -groups},

language = {eng},

number = {1},

pages = {65-77},

title = {Finite groups with globally permutable lattice of subgroups},

url = {http://eudml.org/doc/210751},

volume = {82},

year = {1999},

}

TY - JOUR

AU - Bagiński, C.

AU - Sakowicz, A.

TI - Finite groups with globally permutable lattice of subgroups

JO - Colloquium Mathematicae

PY - 1999

VL - 82

IS - 1

SP - 65

EP - 77

AB - 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.

LA - eng

KW - subgroup lattices; finite modular lattices; globally permutable lattices; finite groups; modular -groups

UR - http://eudml.org/doc/210751

ER -

## References

top- [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. Zbl0217.07201
- [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. Zbl0884.06003
- [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. Zbl0070.25406
- [8] J. G. Thompson, Nonsolvable finite groups all of whose local subgroups are solvable, Bull. Amer. Math. Soc. 74 (1968), 383-434. Zbl0159.30804

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