Planar Groups |
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| Authors: | Colin L. Starr Galen E. Turner III |
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| Affiliation: | (1) Department of Mathematics, Willamette University, 900 State Street, Salem, OR 97302, USA;(2) Program of Mathematics and Statistics, Louisiana Tech University, P.O. Box 3189, Ruston, LA 71272, USA |
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| Abstract: | In abstract algebra courses, teachers are often confronted with the task of drawing subgroup lattices. For purposes of instruction, it is usually desirable that these lattices be planar graphs (with no crossings). We present a characterization of abelian groups with this property. We also resolve the following problem in the abelian case: if the subgroup lattice is required to be drawn hierarchically (that is, in monotonic order of index within the group), when is it possible to draw the lattice without crossings? |
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| Keywords: | graph subgroup lattice planar abelian group |
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