Infinite "Two-Ended" Cayley Diagrams

This page gives the Cayley diagrams of a very few infinite groups. Their presentations are also given. Above each presentation is a short list of elements in bold type: the colours used in the list correspond to the colours of the lines in the diagram.

You can click on any of the diagrams to see a lonrger region of it.

Group Presentation Cayley diagram
ℤ k
< k | >
ℤ r b
< r,b | rbr-1b-1, r2b-3 >
Dℤ r g
< r,g | r2, g2 >
ℤ × C2 k r
< k,r | r2, krk-1r >
Dℤ k r
< k,r | r2, krkr >
Dℤ k r g
< k,r,g | r2, g2, kgr >
ℤ × C2 r g b
< r,g,b | r2, g2, b2, (rg)2, (rb)2 >
Dℤ r g b
< r,g,b | r2, g2, b2, rgrb, (rgb)2 >
Qℤ k r
< k,r | r4, krkr-1 >
Qℤ r g b
< r,g,b | r4, g2, b2, grgr-1, brbr-1 >
Qℤ r g b
< r,g,b | r4, g2, b2, brgr-1, grbr-1 >

Some more Cayley diagrams
and other pages on groups
Copyright N.S.Wedd 2007