#21040 ⟨a, b | ab=aa, bbbb=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. ab ⇒ a2
  2. ba3 ⇒ a4
  3. b4 ⇒ a3
  4. a5 ⇒ a4 
# ab:ab=aa,bbbb=aaa ab
ab=aa
baaa=aaaa
bbbb=aaa
aaaaa=aaaa

Cayley table

Idempotents are shown in bold.

1aba2bab2a3ba2b2ab3a4b2a2b3ab3a2
11aba2bab2a3ba2b2ab3a4b2a2b3ab3a2
aaa2a2a3a3a3a4a4a4a4a4a4a4a4
bbbab2ba2b2ab3a4b2a2b3aa3a4b3a2a4a4
a2a2a3a3a4a4a4a4a4a4a4a4a4a4a4
bababa2ba2a4a4a4a4a4a4a4a4a4a4a4
b2b2b2ab3b2a2b3aa3a4b3a2a4a4a4a4a4a4
a3a3a4a4a4a4a4a4a4a4a4a4a4a4a4
ba2ba2a4a4a4a4a4a4a4a4a4a4a4a4a4
b2ab2ab2a2b2a2a4a4a4a4a4a4a4a4a4a4a4
b3b3b3aa3b3a2a4a4a4a4a4a4a4a4a4a4
a4a4a4a4a4a4a4a4a4a4a4a4a4a4a4
b2a2b2a2a4a4a4a4a4a4a4a4a4a4a4a4a4
b3ab3ab3a2b3a2a4a4a4a4a4a4a4a4a4a4a4
b3a2b3a2a4a4a4a4a4a4a4a4a4a4a4a4a4

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
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
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
1121041⟨a, b | ab=aa, bbbb=aab⟩φ(a) = a, φ(b) = b
1121042⟨a, b | ab=aa, bbbb=aba⟩φ(a) = a, φ(b) = b
1121043⟨a, b | ab=aa, bbbb=abb⟩φ(a) = a, φ(b) = b