#21110 ⟨a, b | bb=aa, abab=aaa⟩

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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. b6 ⇒ b4
  2. ab3 ⇒ b5
  3. b2a ⇒ ab2
  4. a2 ⇒ b2
  5. (ab)2 ⇒ ab2 
# ab:bb=aa,abab=aaa b/a
bbbbbb=bbbb
abbb=bbbbb
bba=abb
aa=bb
abab=abb

Cayley table

Idempotents are shown in bold.

1ababbab2abaab2babb3(ba)2bab2b4b5
11ababbab2abaab2babb3(ba)2bab2b4b5
aab2abb3abaab2bab2b4ab2b5b4b5b4b5
bbbab2babab2b3(ba)2bab2b5b4b5b4b5b4
abababaab2ab2b4b5b4b5b5b4b5b4b5b4
babab3babb4(ba)2bab2b4b5bab2b4b5b4b5b4
b2b2ab2b3b5bab2b4b5b4b4b5b4b5b4b5
abaabab5ab2b4b4b5b4b5b5b4b5b4b5b4
ab2ab2b4b5b5b5b4b5b4b4b5b4b5b4b5
babbab(ba)2bab2bab2b5b4b5b4b4b5b4b5b4b5
b3b3bab2b4b4b4b5b4b5b5b4b5b4b5b4
(ba)2(ba)2b4bab2b5b5b4b5b4b4b5b4b5b4b5
bab2bab2b5b4b4b4b5b4b5b5b4b5b4b5b4
b4b4b4b5b5b5b4b5b4b4b5b4b5b4b5
b5b5b5b4b4b4b5b4b5b5b4b5b4b5b4

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

30 unique, 314 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
105218⟨a, b | aab=bb, bbba=a⟩Finite non-commutative monoid with 14 elements5 iso, 1 anti-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
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 anti-isomorphic instances

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

2 total

Σ#PresentationMapping
1121111⟨a, b | bb=aa, abab=aab⟩φ(a) = b, φ(b) = a
1121113⟨a, b | bb=aa, abab=baa⟩φ(a) = b, φ(b) = a