#3034 ⟨a, b | aa=a, bbbb=ab⟩

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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. b7 ⇒ b4
  2. ab ⇒ b4
  3. a2 ⇒ a 
# ab:aa=a,bbbb=ab b/a
bbbbbbb=bbbb
ab=bbbb
aa=a

Cayley table

Idempotents are shown in bold.

1abbab2b2ab3b3ab4b4ab5b5ab6b6a
11abbab2b2ab3b3ab4b4ab5b5ab6b6a
aaab4b4ab5b5ab6b6ab4b4ab5b5ab6b6a
bbbab2b2ab3b3ab4b4ab5b5ab6b6ab4b4a
bababab5b5ab6b6ab4b4ab5b5ab6b6ab4b4a
b2b2b2ab3b3ab4b4ab5b5ab6b6ab4b4ab5b5a
b2ab2ab2ab6b6ab4b4ab5b5ab6b6ab4b4ab5b5a
b3b3b3ab4b4ab5b5ab6b6ab4b4ab5b5ab6b6a
b3ab3ab3ab4b4ab5b5ab6b6ab4b4ab5b5ab6b6a
b4b4b4ab5b5ab6b6ab4b4ab5b5ab6b6ab4b4a
b4ab4ab4ab5b5ab6b6ab4b4ab5b5ab6b6ab4b4a
b5b5b5ab6b6ab4b4ab5b5ab6b6ab4b4ab5b5a
b5ab5ab5ab6b6ab4b4ab5b5ab6b6ab4b4ab5b5a
b6b6b6ab4b4ab5b5ab6b6ab4b4ab5b5ab6b6a
b6ab6ab6ab4b4ab5b5ab6b6ab4b4ab5b5ab6b6a

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
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
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.

2 total

Σ#PresentationMapping
109179⟨a, b | aa=a, bbbb=aab⟩φ(a) = a, φ(b) = b
1125718⟨a, b | aa=a, bbbb=aaab⟩φ(a) = a, φ(b) = b