#5335 ⟨a, b | aaa=ab, bbb=aa⟩

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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. a7 ⇒ a3
  2. ba2 ⇒ a4
  3. ab ⇒ a3
  4. b3 ⇒ a2 
# ab:aaa=ab,bbb=aa a/b
aaaaaaa=aaa
baa=aaaa
ab=aaa
bbb=aa

Cayley table

Idempotents are shown in bold.

1aba2bab2a3b2aa4a5a6
11aba2bab2a3b2aa4a5a6
aaa2a3a3a4a5a4a6a5a6a3
bbbab2a4b2aa2a5a3a6a3a4
a2a2a3a4a4a5a6a5a3a6a3a4
babaa4a5a5a6a3a6a4a3a4a5
b2b2b2aa2a6a3a4a3a5a4a5a6
a3a3a4a5a5a6a3a6a4a3a4a5
b2ab2aa6a3a3a4a5a4a6a5a6a3
a4a4a5a6a6a3a4a3a5a4a5a6
a5a5a6a3a3a4a5a4a6a5a6a3
a6a6a3a4a4a5a6a5a3a6a3a4

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

29 unique, 477 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
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.

2 total

Σ#PresentationMapping
1116050⟨a, b | aaa=bb, aaab=ba⟩φ(a) = b, φ(b) = a
1116054⟨a, b | aaa=bb, aaba=ba⟩φ(a) = b, φ(b) = a

Other anti-isomorphic instances

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

1 total

Σ#PresentationMapping
1116049⟨a, b | aaa=bb, aaab=ab⟩φ(a) = b, φ(b) = a