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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.
J. Krempa, and A. Sakowicz. "On uniform dimensions of finite groups." Colloquium Mathematicae 89.2 (2001): 223-231. <http://eudml.org/doc/283648>.
@article{J2001, abstract = {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.}, author = {J. Krempa, A. Sakowicz}, journal = {Colloquium Mathematicae}, keywords = {subgroup lattices; strongly balanced lattices; uniform dimensions; globally permutable lattices}, language = {eng}, number = {2}, pages = {223-231}, title = {On uniform dimensions of finite groups}, url = {http://eudml.org/doc/283648}, volume = {89}, year = {2001}, }
TY - JOUR AU - J. Krempa AU - A. Sakowicz TI - On uniform dimensions of finite groups JO - Colloquium Mathematicae PY - 2001 VL - 89 IS - 2 SP - 223 EP - 231 AB - 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. LA - eng KW - subgroup lattices; strongly balanced lattices; uniform dimensions; globally permutable lattices UR - http://eudml.org/doc/283648 ER -