#7143 ⟨a, b | bb=aa, aaab=ba⟩

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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 ⇒ b3
  2. ab6 ⇒ ab2
  3. ba ⇒ ab3
  4. a2 ⇒ b2 
# ab:bb=aa,aaab=ba b/a
bbbbbbb=bbb
abbbbbb=abb
ba=abbb
aa=bb

Cayley table

Idempotents are shown in bold.

1ababb2ab2b3ab3b4ab4b5ab5b6
11ababb2ab2b3ab3b4ab4b5ab5b6
aab2abb3ab2b4ab3b5ab4b6ab5b3ab2
bbab3b2ab4b3ab5b4ab2b5ab3b6ab4b3
ababb5ab2b6ab3b3ab4b4ab5b5ab2b6ab3
b2b2ab2b3ab3b4ab4b5ab5b6ab2b3ab3b4
ab2ab2b4ab3b5ab4b6ab5b3ab2b4ab3b5ab4
b3b3ab5b4ab2b5ab3b6ab4b3ab5b4ab2b5
ab3ab3b3ab4b4ab5b5ab2b6ab3b3ab4b4ab5
b4b4ab4b5ab5b6ab2b3ab3b4ab4b5ab5b6
ab4ab4b6ab5b3ab2b4ab3b5ab4b6ab5b3ab2
b5b5ab3b6ab4b3ab5b4ab2b5ab3b6ab4b3
ab5ab5b5ab2b6ab3b3ab4b4ab5b5ab2b6ab3
b6b6ab2b3ab3b4ab4b5ab5b6ab2b3ab3b4

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

26 unique, 302 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
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
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.

1 total

Σ#PresentationMapping
107146⟨a, b | bb=aa, aaba=ab⟩φ(a) = b, φ(b) = a