#3767 ⟨a, b | aaaa=ab, bbbb=1⟩

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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. a13 ⇒ a
  2. ab ⇒ a4
  3. b4 ⇒ 1 
# ab:aaaa=ab,bbbb=1 a/b
aaaaaaaaaaaaa=a
ab=aaaa
bbbb=1

Right Cayley graph

Left Cayley graph

Others with same cardinality

1 unique, 1 total

Σ#PresentationDescriptionRelated
1112195⟨a, b | aaaa=ab, bbbb=b⟩Finite non-commutative monoid with 52 elements

Other anti-isomorphic instances

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

3 total

Σ#PresentationMapping
105721⟨a, b | aaaa=1, abbbb=b⟩φ(a) = b, φ(b) = bba
1117129⟨a, b | aaaa=1, ababbb=b⟩φ(a) = b, φ(b) = aa
1117133⟨a, b | aaaa=1, abbabb=b⟩φ(a) = b, φ(b) = aa