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1

On strong uniform dimension of locally finite groups

100%

Sakowicz A.

Colloquium Mathematicum

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2003

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tom 95

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nr 2

207-216

EN

We give the description of locally finite groups with strongly balanced subgroup lattices and we prove that the strong uniform dimension of such groups exists. Moreover we show how to determine this dimension.

2

On uniform dimensions of finite groups

63%

Krempa J., Sakowicz A.

Colloquium Mathematicum

|

2001

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tom 89

|

nr 2

223-231

EN

Let G be any finite group and L(G) the lattice of all subgroups of G. If L(G) is strongly balanced (globally permutable) then we observe that the uniform dimension and the strong uniform dimension of L(G) are well defined, and we show how to calculate these dimensions.

3

Finite groups with globally permutable lattice of subgroups

63%

Bagiński C., Sakowicz A.

Colloquium Mathematicum

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1999

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tom 82

|

nr 1

65-77

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.

Ograniczanie wyników

3 Colloquium Mathematicum

3 Sakowicz A.

1 Bagiński C.

1 Krempa J.

1 2003

1 2001

1 1999

On strong uniform dimension of locally finite groups

On uniform dimensions of finite groups

Finite groups with globally permutable lattice of subgroups