Finite groups with globally permutable lattice of subgroups

C. Bagiński; A. Sakowicz

Colloquium Mathematicae (1999)

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

Abstract

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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.

How to cite

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Bagiński, 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

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  1. [1] G. Birkhoff, Lattice Theory, 3rd ed., Amer. Math. Soc., Providence, RI, 1967. 
  2. [2] D. Gorenstein, Finite Simple Groups. An Introduction to Their Classification}, Plenum Press, New York, 1982. 
  3. [3] B. Huppert, Endliche Gruppen I, Springer, Berlin, 1983. Zbl0217.07201
  4. [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. [5] E. Lukács, Modularity of some three-generator sublattices in subgroup lattices, Comm. Algebra 15 (1987), 2073-2080. 
  6. [6] R. Schmidt, Subgroup Lattices of Groups, de Gruyter, Berlin, 1994. 
  7. [7] M. Suzuki, Structure of a Group and the Structure of its Lattice of Subgroups, Springer, Berlin, 1956. Zbl0070.25406
  8. [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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