#4683 ⟨a, b | aaab=b, abba=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. b7 ⇒ b
  2. ab ⇒ b5
  3. b6a ⇒ a
  4. a2 ⇒ b4a 
# ab:aaab=b,abba=a b/a
bbbbbbb=b
ab=bbbbb
bbbbbba=a
aa=bbbba

Cayley table

Idempotents are shown in bold.

1abbab2b2ab3b3ab4b4ab5b5ab6
11abbab2b2ab3b3ab4b4ab5b5ab6
aab4ab5b5ab6abbab2b2ab3b3ab4
bbbab2b2ab3b3ab4b4ab5b5ab6ab
babab5ab6abbab2b2ab3b3ab4b4ab5
b2b2b2ab3b3ab4b4ab5b5ab6abbab2
b2ab2aabbab2b2ab3b3ab4b4ab5b5ab6
b3b3b3ab4b4ab5b5ab6abbab2b2ab3
b3ab3abab2b2ab3b3ab4b4ab5b5ab6ab
b4b4b4ab5b5ab6abbab2b2ab3b3ab4
b4ab4ab2ab3b3ab4b4ab5b5ab6abbab2
b5b5b5ab6abbab2b2ab3b3ab4b4ab5
b5ab5ab3ab4b4ab5b5ab6abbab2b2ab3
b6b6abbab2b2ab3b3ab4b4ab5b5ab6

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

26 unique, 287 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
105065⟨a, b | aaa=ab, babb=b⟩Finite non-commutative monoid with 13 elements7 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.

15 total

Σ#PresentationMapping
104689⟨a, b | aaab=b, baba=a⟩φ(a) = a, φ(b) = b
104693⟨a, b | aaab=b, bbaa=a⟩φ(a) = a, φ(b) = b
106410⟨a, b | aab=b, abbba=a⟩φ(a) = bbb, φ(b) = ba
106426⟨a, b | aab=b, babba=a⟩φ(a) = bbb, φ(b) = ba
106434⟨a, b | aab=b, bbaba=a⟩φ(a) = bbb, φ(b) = ba
106438⟨a, b | aab=b, bbbaa=a⟩φ(a) = bbb, φ(b) = ba
1114485⟨a, b | aaab=b, aabba=a⟩φ(a) = a, φ(b) = bbbbb
1114497⟨a, b | aaab=b, abbaa=a⟩φ(a) = a, φ(b) = bbbbb
1114509⟨a, b | aaab=b, baaba=a⟩φ(a) = a, φ(b) = bbbbb
1114521⟨a, b | aaab=b, bbaaa=a⟩φ(a) = a, φ(b) = bbbbb
1119004⟨a, b | aab=b, ababba=a⟩φ(a) = bbb, φ(b) = a
1119012⟨a, b | aab=b, abbaba=a⟩φ(a) = bbb, φ(b) = a
1119044⟨a, b | aab=b, bababa=a⟩φ(a) = bbb, φ(b) = a
1119048⟨a, b | aab=b, babbaa=a⟩φ(a) = bbb, φ(b) = a
1119064⟨a, b | aab=b, bbabaa=a⟩φ(a) = bbb, 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
1124461⟨a, b | ab=a, baaaaaa=b⟩φ(a) = b, φ(b) = bba