#5065 ⟨a, b | aaa=ab, babb=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. a8 ⇒ a3
  2. ba5 ⇒ b
  3. ab ⇒ a3
  4. b2 ⇒ ba2 
# ab:aaa=ab,babb=b a/b
aaaaaaaa=aaa
baaaaa=b
ab=aaa
bb=baa

Cayley table

Idempotents are shown in bold.

1aba2baa3ba2a4ba3a5ba4a6a7
11aba2baa3ba2a4ba3a5ba4a6a7
aaa2a3a3a4a4a5a5a6a6a7a7a3
bbbaba2ba2ba3ba3ba4ba4bbbababa2
a2a2a3a4a4a5a5a6a6a7a7a3a3a4
bababa2ba3ba3ba4ba4bbbababa2ba2ba3
a3a3a4a5a5a6a6a7a7a3a3a4a4a5
ba2ba2ba3ba4ba4bbbababa2ba2ba3ba3ba4
a4a4a5a6a6a7a7a3a3a4a4a5a5a6
ba3ba3ba4bbbababa2ba2ba3ba3ba4ba4b
a5a5a6a7a7a3a3a4a4a5a5a6a6a7
ba4ba4bbababa2ba2ba3ba3ba4ba4bbba
a6a6a7a3a3a4a4a5a5a6a6a7a7a3
a7a7a3a4a4a5a5a6a6a7a7a3a3a4

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

26 unique, 296 total

Σ#PresentationDescriptionRelated
91328⟨a, b | aaaa=b, abbb=1⟩Isomorphic to ℤ13189 iso
92118⟨a, b | aba=b, baab=a⟩Finite non-commutative monoid with 13 elements4 iso
104642⟨a, b | aaaa=b, abbb=a⟩Isomorphic to ℕ(13 = 1)10 iso
104643⟨a, b | aaaa=b, abbb=b⟩Isomorphic to ℕ(13 = 4)6 iso
104683⟨a, b | aaab=b, abba=a⟩Finite non-commutative monoid with 13 elements15 iso, 1 anti-iso
105334⟨a, b | aaa=ab, bba=bb⟩Finite non-commutative monoid with 13 elements
105336⟨a, b | aaa=ab, bbb=ab⟩Finite non-commutative monoid with 13 elements1 iso
105337⟨a, b | aaa=ab, bbb=ba⟩Finite non-commutative monoid with 13 elements
105340⟨a, b | aaa=bb, aab=ba⟩Finite non-commutative monoid with 13 elements
106305⟨a, b | aaa=b, abbbb=b⟩Isomorphic to ℕ(13 = 3)2 iso
107143⟨a, b | bb=aa, aaab=ba⟩Finite non-commutative monoid with 13 elements1 iso
1112240⟨a, b | aaab=aa, bbbb=a⟩Isomorphic to ℕ(13 = 8)1 iso
1112268⟨a, b | aaab=ab, bbbb=a⟩Isomorphic to ℕ(13 = 5)3 iso
1112324⟨a, b | aaab=bb, bbbb=a⟩Isomorphic to ℕ(13 = 2)14 iso
1114647⟨a, b | aaba=b, babbb=a⟩Finite commutative monoid with 13 elements2 iso
1115520⟨a, b | aaa=bb, aabbb=b⟩Finite commutative monoid with 13 elements2 iso
1116012⟨a, b | aaa=ab, abbb=bb⟩Finite non-commutative monoid with 13 elements
1116069⟨a, b | aaa=bb, abbb=ba⟩Finite non-commutative monoid with 13 elements1 anti-iso
1116205⟨a, b | aab=ab, bbbb=aa⟩Finite non-commutative monoid with 13 elements1 iso, 1 anti-iso
1116459⟨a, b | aba=bb, abbb=aa⟩Finite non-commutative monoid with 13 elements1 iso
1116506⟨a, b | aab=ab, bbb=aaa⟩Finite non-commutative monoid with 13 elements1 iso
1116515⟨a, b | aab=ba, bbb=aaa⟩Finite non-commutative monoid with 13 elements
1118958⟨a, b | aab=a, bbbbbb=a⟩Isomorphic to ℕ(13 = 6)4 iso
1120046⟨a, b | aab=a, bbbb=bba⟩Finite non-commutative monoid with 13 elements
1120927⟨a, b | ab=aa, aaaa=bbb⟩Finite non-commutative monoid with 13 elements7 iso
1120991⟨a, b | ab=aa, baaa=bbb⟩Finite non-commutative monoid with 13 elements3 iso

Other isomorphic instances

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

7 total

Σ#PresentationMapping
105069⟨a, b | aaa=ab, bbab=b⟩φ(a) = a, φ(b) = b
105071⟨a, b | aaa=ab, bbba=b⟩φ(a) = a, φ(b) = b
1115476⟨a, b | aaa=ab, baaab=b⟩φ(a) = a, φ(b) = b
1115478⟨a, b | aaa=ab, baaba=b⟩φ(a) = a, φ(b) = b
1115482⟨a, b | aaa=ab, babaa=b⟩φ(a) = a, φ(b) = b
1115490⟨a, b | aaa=ab, bbaaa=b⟩φ(a) = a, φ(b) = b
1119991⟨a, b | aab=a, baaa=bbb⟩φ(a) = baa, φ(b) = a