#1345 ⟨a, b | aaab=a, 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. a9 ⇒ a
  2. ab ⇒ a7
  3. b4 ⇒ 1 
# ab:aaab=a,bbbb=1 a/b
aaaaaaaaa=a
ab=aaaaaaa
bbbb=1

Right Cayley graph

Left Cayley graph

Others with same cardinality

4 unique, 28 total

Σ#PresentationDescriptionRelated
92300⟨a, b | aaa=1, ababbb=1⟩Finite non-Abelian group with 36 elements23 iso
105073⟨a, b | aaa=ab, bbbb=b⟩Finite non-commutative monoid with 36 elements1 iso
1116044⟨a, b | aaa=ab, bbbb=bb⟩Finite non-commutative monoid with 36 elements
1118959⟨a, b | aab=a, bbbbbb=b⟩Finite non-commutative monoid with 36 elements

Other isomorphic instances

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

5 total

Σ#PresentationMapping
91465⟨a, b | aaa=ab, bbbb=1⟩φ(a) = a, φ(b) = bbb
1110725⟨a, b | aaab=abb, bbbb=1⟩φ(a) = a, φ(b) = bbb
1111062⟨a, b | abbb=aaa, bbbb=1⟩φ(a) = a, φ(b) = b
1117662⟨a, b | aaaa=1, abbba=ab⟩φ(a) = b, φ(b) = a
1117673⟨a, b | aaaa=1, baabb=ba⟩φ(a) = b, φ(b) = a

Other anti-isomorphic instances

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

8 total

Σ#PresentationMapping
1110753⟨a, b | aaab=bab, bbbb=1⟩φ(a) = a, φ(b) = bbb
1117103⟨a, b | aaaa=1, aaabbb=b⟩φ(a) = bbb, φ(b) = a
1117123⟨a, b | aaaa=1, abaabb=b⟩φ(a) = bbb, φ(b) = a
1117125⟨a, b | aaaa=1, ababab=b⟩φ(a) = bbb, φ(b) = a
1117131⟨a, b | aaaa=1, abbaab=b⟩φ(a) = bbb, φ(b) = a
1117643⟨a, b | aaaa=1, aabbb=ab⟩φ(a) = b, φ(b) = a
1117672⟨a, b | aaaa=1, baabb=ab⟩φ(a) = b, φ(b) = a
1117676⟨a, b | aaaa=1, babab=ab⟩φ(a) = b, φ(b) = a