#21046 ⟨a, b | ab=aa, bbbb=bba⟩

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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 ⇒ b5
  2. ab4 ⇒ ab3
  3. b2a ⇒ b4
  4. a2 ⇒ ab
  5. aba ⇒ ab2 
# ab:ab=aa,bbbb=bba b/a
bbbbbb=bbbbb
abbbb=abbb
bba=bbbb
aa=ab
aba=abb

Cayley table

Idempotents are shown in bold.

1ababbab2ab2babb3ab3bab2b4bab3b5
11ababbab2ab2babb3ab3bab2b4bab3b5
aaababab2ab2ab2ab3ab3ab3ab3ab3ab3ab3ab3
bbbab2babb4b3bab2b5b4bab3b5b5b5b5
ababab2ab2ab3ab3ab3ab3ab3ab3ab3ab3ab3ab3ab3
babababbabbab2bab2bab2bab3bab3bab3bab3bab3bab3bab3bab3
b2b2b4b3b5b5b4b5b5b5b5b5b5b5b5
ab2ab2ab3ab3ab3ab3ab3ab3ab3ab3ab3ab3ab3ab3ab3
babbabbab2bab2bab3bab3bab3bab3bab3bab3bab3bab3bab3bab3bab3
b3b3b5b4b5b5b5b5b5b5b5b5b5b5b5
ab3ab3ab3ab3ab3ab3ab3ab3ab3ab3ab3ab3ab3ab3ab3
bab2bab2bab3bab3bab3bab3bab3bab3bab3bab3bab3bab3bab3bab3bab3
b4b4b5b5b5b5b5b5b5b5b5b5b5b5b5
bab3bab3bab3bab3bab3bab3bab3bab3bab3bab3bab3bab3bab3bab3bab3
b5b5b5b5b5b5b5b5b5b5b5b5b5b5b5

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

30 unique, 316 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
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