#1907 ⟨a, b | aab=a, bbbbb=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. a6 ⇒ a
  2. ab ⇒ a5
  3. b5 ⇒ 1 
# ab:aab=a,bbbbb=1 a/b
aaaaaa=a
ab=aaaaa
bbbbb=1

Right Cayley graph

Left Cayley graph

Others with same cardinality

8 unique, 108 total

Σ#PresentationDescriptionRelated
91470⟨a, b | aaa=bb, abab=1⟩Finite non-Abelian group with 30 elements73 iso
92443⟨a, b | aaa=1, abbbb=b⟩Finite non-commutative monoid with 30 elements14 iso, 5 anti-iso
106560⟨a, b | aaa=a, bbbb=ab⟩Finite non-commutative monoid with 30 elements
107013⟨a, b | ab=aa, bbbbb=b⟩Finite non-commutative monoid with 30 elements
1111058⟨a, b | abba=bbb, baba=1⟩Finite non-Abelian group with 30 elements8 iso
1113115⟨a, b | bbb=aaa, aaba=b⟩Finite non-commutative monoid with 30 elements
1115979⟨a, b | aaa=aa, bbbb=ab⟩Finite non-commutative monoid with 30 elements
1120847⟨a, b | ab=aa, bbbbb=bb⟩Finite non-commutative monoid with 30 elements

Other isomorphic instances

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

11 total

Σ#PresentationMapping
92155⟨a, b | ab=aa, bbbbb=1⟩φ(a) = a, φ(b) = bbbb
104541⟨a, b | aabb=a, bbbbb=1⟩φ(a) = a, φ(b) = bbb
104573⟨a, b | abab=a, bbbbb=1⟩φ(a) = a, φ(b) = bbb
105001⟨a, b | aba=ab, bbbbb=1⟩φ(a) = ba, φ(b) = b
1111448⟨a, b | aabbb=a, bbbbb=1⟩φ(a) = aaa, φ(b) = b
1111533⟨a, b | ababb=a, bbbbb=1⟩φ(a) = aaa, φ(b) = b
1111549⟨a, b | abbab=a, bbbbb=1⟩φ(a) = aaa, φ(b) = b
1112096⟨a, b | abba=ab, aaaaa=1⟩φ(a) = b, φ(b) = a
1112127⟨a, b | abba=ab, bbbbb=1⟩φ(a) = a, φ(b) = b
1112772⟨a, b | abb=aba, aaaaa=1⟩φ(a) = bbbb, φ(b) = a
1112803⟨a, b | abb=aba, bbbbb=1⟩φ(a) = a, φ(b) = bbbb

Other anti-isomorphic instances

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

4 total

Σ#PresentationMapping
104918⟨a, b | aab=bb, aaaaa=1⟩φ(a) = b, φ(b) = aaa
1111788⟨a, b | aaab=bb, aaaaa=1⟩φ(a) = bbb, φ(b) = a
1111980⟨a, b | aabb=ab, aaaaa=1⟩φ(a) = b, φ(b) = a
1112756⟨a, b | abb=aab, aaaaa=1⟩φ(a) = b, φ(b) = bba