Maths - Hasse Diagrams

A Hasse diagram is used for partially ordered sets, however here it is used to show subgroup structure of a group, that is a lattice of subgroups.

For example the Hasse diagram for the D4 group, that is the dihedral group of rotations and reflections of a square.

group d4 hasse diagram

So the whole D4 group has 8 permutations and this has 9 subgroups:

The Hasse represents a lattice which is explained on this page.


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see also:
  • For an introduction to Cayley tables see this page.
  • Generating cayley tables for hypercomplex numbers see this page.
Correspondence about this page

Book Shop - Further reading.

Where I can, I have put links to Amazon for books that are relevant to the subject, click on the appropriate country flag to get more details of the book or to buy it from them.

flag flag flag flag flag flag Symmetry and the Monster - This is a popular science type book which traces the history leading up to the discovery of the largest symmetry groups.

Terminology and Notation

Specific to this page here:

 

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