#19070 ⟨a, b | aab=b, bbabbb=a⟩

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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. ba ⇒ ab
  2. a3 ⇒ a
  3. a2b ⇒ b
  4. b5 ⇒ a2 
# ab:aab=b,bbabbb=a ab
ba=ab
aaa=a
aab=b
bbbbb=aa

Staircase diagram

Cayley table

Idempotents are shown in bold.

1aba2abb2ab2b3ab3b4ab4
11aba2abb2ab2b3ab3b4ab4
aaa2ababab2b2ab3b3ab4b4
bbabb2bab2b3ab3b4ab4a2a
a2a2aba2abb2ab2b3ab3b4ab4
ababbab2abb2ab3b3ab4b4aa2
b2b2ab2b3b2ab3b4ab4a2abab
ab2ab2b2ab3ab2b3ab4b4aa2abb
b3b3ab3b4b3ab4a2ababb2ab2
ab3ab3b3ab4ab3b4aa2abbab2b2
b4b4ab4a2b4ababb2ab2b3ab3
ab4ab4b4aab4a2abbab2b2ab3b3

Right Cayley graph

Idempotents are shown in bold.

Others with same cardinality

29 unique, 476 total

Σ#PresentationDescriptionRelated
91472⟨a, b | aaa=bb, abbb=1⟩Isomorphic to ℤ11259 iso
104155⟨a, b | abb=aaa, bba=b⟩Finite non-commutative monoid with 11 elements4 iso
105086⟨a, b | aaa=bb, abbb=a⟩Finite commutative monoid with 11 elements11 iso
105087⟨a, b | aaa=bb, abbb=b⟩Finite commutative monoid with 11 elements3 iso
105111⟨a, b | aab=aa, baaa=b⟩Finite non-commutative monoid with 11 elements7 iso
105322⟨a, b | aaa=ab, abb=bb⟩Finite non-commutative monoid with 11 elements3 iso
105335⟨a, b | aaa=ab, bbb=aa⟩Finite non-commutative monoid with 11 elements2 iso, 1 anti-iso
105410⟨a, b | aab=bb, bab=aa⟩Finite non-commutative monoid with 11 elements2 iso
106292⟨a, b | aaa=b, aabbb=a⟩Isomorphic to ℕ(11 = 1)35 iso
106293⟨a, b | aaa=b, aabbb=b⟩Isomorphic to ℕ(11 = 3)11 iso
106380⟨a, b | aab=a, bbbbb=a⟩Isomorphic to ℕ(11 = 5)1 iso
106834⟨a, b | aba=b, abb=aaa⟩Finite non-commutative monoid with 11 elements
107114⟨a, b | ab=aa, bbbb=aa⟩Finite non-commutative monoid with 11 elements1 iso
107116⟨a, b | ab=aa, bbbb=ba⟩Finite non-commutative monoid with 11 elements
108691⟨a, b | aa=b, abbbbb=b⟩Isomorphic to ℕ(11 = 2)32 iso
108777⟨a, b | ab=a, baaaaa=b⟩Finite non-commutative monoid with 11 elements20 iso, 5 anti-iso
109083⟨a, b | ab=a, bbaaa=bb⟩Finite non-commutative monoid with 11 elements4 iso
1112179⟨a, b | aaaa=ab, abbb=b⟩Isomorphic to ℕ(11 = 4)20 iso
1115607⟨a, b | aab=aa, bbbbb=a⟩Isomorphic to ℕ(11 = 10)1 iso
1115671⟨a, b | aab=ab, bbbbb=a⟩Isomorphic to ℕ(11 = 6)8 iso
1116148⟨a, b | aab=ab, aaaa=bb⟩Finite non-commutative monoid with 11 elements1 iso
1116212⟨a, b | aab=ba, aaaa=bb⟩Finite non-commutative monoid with 11 elements
1118715⟨a, b | aaa=a, aabbba=b⟩Finite non-commutative monoid with 11 elements
1120096⟨a, b | aab=b, abba=aaa⟩Finite non-commutative monoid with 11 elements1 iso
1120112⟨a, b | aab=b, baaa=aaa⟩Finite non-commutative monoid with 11 elements
1120168⟨a, b | aab=b, bbbb=aaa⟩Finite commutative monoid with 11 elements
1120885⟨a, b | bb=aa, aaaaa=ab⟩Finite non-commutative monoid with 11 elements7 iso, 8 anti-iso
1125539⟨a, b | ab=a, baaaa=bbb⟩Finite non-commutative monoid with 11 elements
1125635⟨a, b | ab=a, bbbaa=bbb⟩Finite non-commutative monoid with 11 elements

Other isomorphic instances

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

4 total

Σ#PresentationMapping
1119078⟨a, b | aab=b, bbbabb=a⟩φ(a) = a, φ(b) = b
1119210⟨a, b | aba=b, abbbbb=a⟩φ(a) = a, φ(b) = b
1119224⟨a, b | aba=b, babbbb=a⟩φ(a) = a, φ(b) = b
1119228⟨a, b | aba=b, bbabbb=a⟩φ(a) = a, φ(b) = b