#5111 ⟨a, b | aab=aa, baaa=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. b2 ⇒ b
  2. a2b ⇒ a2
  3. bab ⇒ ba
  4. ba3 ⇒ b
  5. a5 ⇒ a2 
# ab:aab=aa,baaa=b ab
bb=b
aab=aa
bab=ba
baaa=b
aaaaa=aa

Cayley table

Idempotents are shown in bold.

1aba2abbaa3ababa2a4aba2
11aba2abbaa3ababa2a4aba2
aaa2aba3a2abaa4a3aba2a2a4
bbbabba2bababba2ba2bab
a2a2a3a2a4a3a3a2a4a4a3a2
abababaababa2abaabaababa2aba2abaab
bababa2babba2ba2babbba2ba
a3a3a4a3a2a4a4a3a2a2a4a3
abaabaaba2abaababa2aba2abaabababa2aba
ba2ba2bba2babbba2bababba2
a4a4a2a4a3a2a2a4a3a3a2a4
aba2aba2ababa2abaabababa2abaabaababa2

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

29 unique, 473 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
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
1119070⟨a, b | aab=b, bbabbb=a⟩Finite commutative monoid with 11 elements4 iso
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.

7 total

Σ#PresentationMapping
1112227⟨a, b | aaab=aa, baaa=b⟩φ(a) = a, φ(b) = baa
1112337⟨a, b | aaba=aa, baaa=b⟩φ(a) = a, φ(b) = baa
1115580⟨a, b | aab=aa, baaab=b⟩φ(a) = a, φ(b) = b
1115582⟨a, b | aab=aa, baaba=b⟩φ(a) = a, φ(b) = b
1115586⟨a, b | aab=aa, babaa=b⟩φ(a) = a, φ(b) = b
1115594⟨a, b | aab=aa, bbaaa=b⟩φ(a) = a, φ(b) = b
1119475⟨a, b | aab=a, bbaaa=bb⟩φ(a) = baa, φ(b) = a