#5218 ⟨a, b | aab=bb, bbba=a⟩

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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. a7 ⇒ a
  2. ba ⇒ a3
  3. b2 ⇒ a2b 
# ab:aab=bb,bbba=a a/b
aaaaaaa=a
ba=aaa
bb=aab

Cayley table

Idempotents are shown in bold.

1aba2aba3a2ba4a3ba5a4ba6a5ba6b
11aba2aba3a2ba4a3ba5a4ba6a5ba6b
aaa2aba3a2ba4a3ba5a4ba6a5baa6bab
bba3a2ba4a3ba5a4ba6a5baa6ba2aba2b
a2a2a3a2ba4a3ba5a4ba6a5baa6ba2aba2b
ababa4a3ba5a4ba6a5baa6ba2aba3a2ba3b
a3a3a4a3ba5a4ba6a5baa6ba2aba3a2ba3b
a2ba2ba5a4ba6a5baa6ba2aba3a2ba4a3ba4b
a4a4a5a4ba6a5baa6ba2aba3a2ba4a3ba4b
a3ba3ba6a5baa6ba2aba3a2ba4a3ba5a4ba5b
a5a5a6a5baa6ba2aba3a2ba4a3ba5a4ba5b
a4ba4baa6ba2aba3a2ba4a3ba5a4ba6a5ba6b
a6a6aa6ba2aba3a2ba4a3ba5a4ba6a5ba6b
a5ba5ba2aba3a2ba4a3ba5a4ba6a5baa6bab
a6ba6ba3a2ba4a3ba5a4ba6a5baa6ba2aba2b

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

30 unique, 310 total

Σ#PresentationDescriptionRelated
81123⟨a, b | aa=1, abbbb=b⟩Finite non-commutative monoid with 14 elements42 iso, 17 anti-iso
91682⟨a, b | aba=bb, bab=a⟩Finite non-commutative monoid with 14 elements1 iso
93034⟨a, b | aa=a, bbbb=ab⟩Finite non-commutative monoid with 14 elements2 iso
103773⟨a, b | aaaa=bb, abbb=1⟩Isomorphic to ℤ14165 iso
105404⟨a, b | aab=bb, aba=aa⟩Finite non-commutative monoid with 14 elements1 iso
106718⟨a, b | aab=b, bbba=aa⟩Finite non-commutative monoid with 14 elements2 iso
1112183⟨a, b | aaaa=ab, baab=b⟩Finite non-commutative monoid with 14 elements3 iso
1112206⟨a, b | aaaa=bb, abbb=a⟩Finite commutative monoid with 14 elements1 iso
1112207⟨a, b | aaaa=bb, abbb=b⟩Finite commutative monoid with 14 elements1 iso
1112441⟨a, b | aabb=aa, baab=b⟩Finite non-commutative monoid with 14 elements3 iso
1112499⟨a, b | abab=aa, abba=b⟩Finite non-commutative monoid with 14 elements
1114383⟨a, b | aaaa=b, aabbb=a⟩Isomorphic to ℕ(14 = 1)15 iso
1114384⟨a, b | aaaa=b, aabbb=b⟩Isomorphic to ℕ(14 = 4)5 iso
1115532⟨a, b | aaa=bb, abbbb=b⟩Isomorphic to ℕ(14 = 3)11 iso
1115539⟨a, b | aaa=bb, babbb=a⟩Finite commutative monoid with 14 elements
1116020⟨a, b | aaa=ab, baab=bb⟩Finite non-commutative monoid with 14 elements1 iso
1116079⟨a, b | aaa=bb, bbbb=ab⟩Finite non-commutative monoid with 14 elements
1116293⟨a, b | aab=bb, abab=aa⟩Finite non-commutative monoid with 14 elements
1116470⟨a, b | aba=bb, bbbb=aa⟩Finite non-commutative monoid with 14 elements
1119552⟨a, b | aab=b, abbaa=aa⟩Finite non-commutative monoid with 14 elements2 iso
1120844⟨a, b | ab=aa, bbbbb=aa⟩Finite non-commutative monoid with 14 elements1 iso
1120846⟨a, b | ab=aa, bbbbb=ba⟩Finite non-commutative monoid with 14 elements
1121023⟨a, b | ab=aa, bbaa=bbb⟩Finite non-commutative monoid with 14 elements1 iso
1121040⟨a, b | ab=aa, bbbb=aaa⟩Finite non-commutative monoid with 14 elements3 iso
1121044⟨a, b | ab=aa, bbbb=baa⟩Finite non-commutative monoid with 14 elements1 iso
1121046⟨a, b | ab=aa, bbbb=bba⟩Finite non-commutative monoid with 14 elements
1121110⟨a, b | bb=aa, abab=aaa⟩Finite non-commutative monoid with 14 elements2 anti-iso
1124186⟨a, b | aa=a, bbbbbbb=a⟩Isomorphic to ℕ(14 = 7)
1124331⟨a, b | aa=b, bbbbbbb=b⟩Isomorphic to ℕ(14 = 2)
1125055⟨a, b | ab=a, bbaaaa=bb⟩Finite non-commutative monoid with 14 elements

Other isomorphic instances

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

5 total

Σ#PresentationMapping
1115749⟨a, b | aab=bb, aabba=a⟩φ(a) = a, φ(b) = b
1115761⟨a, b | aab=bb, abbaa=a⟩φ(a) = a, φ(b) = b
1115773⟨a, b | aab=bb, baaba=a⟩φ(a) = a, φ(b) = b
1115777⟨a, b | aab=bb, babaa=a⟩φ(a) = a, φ(b) = b
1115785⟨a, b | aab=bb, bbaaa=a⟩φ(a) = a, φ(b) = b

Other anti-isomorphic instances

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

1 total

Σ#PresentationMapping
1112503⟨a, b | abab=aa, baaa=b⟩φ(a) = b, φ(b) = aaa