#5421 ⟨a, b | aba=bb, bab=aa⟩

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Properties

Element profile

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. a10 ⇒ a4
  2. ba8 ⇒ ba2
  3. a2ba6 ⇒ a2b
  4. a3b ⇒ ba3
  5. b2 ⇒ aba
  6. bab ⇒ a2
  7. ba2b ⇒ a2ba5 
# ab:aba=bb,bab=aa a/b
aaaaaaaaaa=aaaa
baaaaaaaa=baa
aabaaaaaa=aab
aaab=baaa
bb=aba
bab=aa
baab=aabaaaaa

Right Cayley graph

Left Cayley graph

Others with same cardinality

2 unique, 19 total

Σ#PresentationDescriptionRelated
93385⟨a, b | aa=1, abbbba=b⟩Finite non-commutative monoid with 32 elements17 iso
1115515⟨a, b | aaa=bb, aabab=a⟩Finite non-commutative monoid with 32 elements