#12183 ⟨a, b | aaaa=ab, baab=b⟩

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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 ⇒ a4
  2. ba5 ⇒ b
  3. ab ⇒ a4
  4. b2 ⇒ ba3 
# ab:aaaa=ab,baab=b a/b
aaaaaaaaa=aaaa
baaaaa=b
ab=aaaa
bb=baaa

Cayley table

Idempotents are shown in bold.

1aba2baa3ba2a4ba3a5ba4a6a7a8
11aba2baa3ba2a4ba3a5ba4a6a7a8
aaa2a4a3a5a4a6a5a7a6a8a7a8a4
bbbaba3ba2ba4ba3bba4babba2baba2ba3
a2a2a3a5a4a6a5a7a6a8a7a4a8a4a5
bababa2ba4ba3bba4babba2baba3ba2ba3ba4
a3a3a4a6a5a7a6a8a7a4a8a5a4a5a6
ba2ba2ba3bba4babba2baba3ba2ba4ba3ba4b
a4a4a5a7a6a8a7a4a8a5a4a6a5a6a7
ba3ba3ba4babba2baba3ba2ba4ba3bba4bba
a5a5a6a8a7a4a8a5a4a6a5a7a6a7a8
ba4ba4bba2baba3ba2ba4ba3bba4babbaba2
a6a6a7a4a8a5a4a6a5a7a6a8a7a8a4
a7a7a8a5a4a6a5a7a6a8a7a4a8a4a5
a8a8a4a6a5a7a6a8a7a4a8a5a4a5a6

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

30 unique, 313 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
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.

3 total

Σ#PresentationMapping
1112185⟨a, b | aaaa=ab, baba=b⟩φ(a) = a, φ(b) = b
1112189⟨a, b | aaaa=ab, bbaa=b⟩φ(a) = a, φ(b) = b
1120044⟨a, b | aab=a, bbbb=baa⟩φ(a) = ba, φ(b) = a