#4623 ⟨a, b | aaaa=a, abba=b⟩

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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. ba2 ⇒ ab2
  2. b2a ⇒ a2b
  3. a4 ⇒ a
  4. a3b ⇒ b
  5. bab2 ⇒ a2ba
  6. b5 ⇒ a(ba)2
  7. (ba)3 ⇒ (ab)3 
# ab:aaaa=a,abba=b ab
baa=abb
bba=aab
aaaa=a
aaab=b
babb=aaba
bbbbb=ababa
bababa=ababab

Right Cayley graph

Left Cayley graph

Others with same cardinality

2 unique, 7 total

Σ#PresentationDescriptionRelated
104625⟨a, b | aaaa=a, abbb=b⟩Finite non-commutative monoid with 28 elements2 iso
104691⟨a, b | aaab=b, babb=a⟩Finite non-commutative monoid with 28 elements3 iso

Other isomorphic instances

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

1 total

Σ#PresentationMapping
1114348⟨a, b | aaaa=a, ababa=b⟩φ(a) = a, φ(b) = aab