#16069 ⟨a, b | aaa=bb, abbb=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. b5 ⇒ b3
  2. ab4 ⇒ ab2
  3. ba ⇒ ab3
  4. a3 ⇒ b2 
# ab:aaa=bb,abbb=ba b/a
bbbbb=bbb
abbbb=abb
ba=abbb
aaa=bb

Cayley table

Idempotents are shown in bold.

1aba2abb2a2bab2b3a2b2ab3b4a2b3
11aba2abb2a2bab2b3a2b2ab3b4a2b3
aaa2abb2a2bab2b3a2b2ab3b4a2b3ab2b3
bbab3b2a2b3ab2b3a2b2ab3b4a2b3ab2b3a2b2
a2a2b2a2bab2b3a2b2ab3b4a2b3ab2b3a2b2ab3
ababa2b3ab2b3a2b2ab3b4a2b3ab2b3a2b2ab3b4
b2b2ab2b3a2b2ab3b4a2b3ab2b3a2b2ab3b4a2b3
a2ba2bb3a2b2ab3b4a2b3ab2b3a2b2ab3b4a2b3ab2
ab2ab2a2b2ab3b4a2b3ab2b3a2b2ab3b4a2b3ab2b3
b3b3ab3b4a2b3ab2b3a2b2ab3b4a2b3ab2b3a2b2
a2b2a2b2b4a2b3ab2b3a2b2ab3b4a2b3ab2b3a2b2ab3
ab3ab3a2b3ab2b3a2b2ab3b4a2b3ab2b3a2b2ab3b4
b4b4ab2b3a2b2ab3b4a2b3ab2b3a2b2ab3b4a2b3
a2b3a2b3b3a2b2ab3b4a2b3ab2b3a2b2ab3b4a2b3ab2

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
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
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 anti-isomorphic instances

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

1 total

Σ#PresentationMapping
1116075⟨a, b | aaa=bb, babb=ab⟩φ(a) = a, φ(b) = b