#10664 ⟨a, b | aaaa=bbb, abab=1⟩

Properties

Elements

Elements in the center commute with all other elements.
The order of x is the least n such that xn = 1.

Complete rewriting system

Format:
Word to reduce:
Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Reduction strategy:
Path to normal form: 1
1
  1. a56 ⇒ 1
  2. a4bba4
  3. b2aba5
  4. baba55
  5. ba2ba3ba47
  6. aba3bba3ba43
# ab:aaaa=bbb,abab=1 a/b
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa=1
aaaab=baaaa
bb=abaaaaa
bab=aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
baab=aaabaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
abaaab=baaabaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

Right Cayley graph

Left Cayley graph