#14647 ⟨a, b | aaba=b, babbb=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. ba ⇒ ab
  2. a4 ⇒ a
  3. a3b ⇒ b
  4. b4 ⇒ a3 
# ab:aaba=b,babbb=a ab
ba=ab
aaaa=a
aaab=b
bbbb=aaa

Staircase diagram

Cayley table

Idempotents are shown in bold.

1aba2abb2a3a2bab2b3a2b2ab3a2b3
11aba2abb2a3a2bab2b3a2b2ab3a2b3
aaa2aba3a2bab2aba2b2ab3b2a2b3b3
bbabb2a2bab2b3ba2b2ab3a3a2b3aa2
a2a2a3a2baba2b2a2abb2a2b3ab2b3ab3
ababa2bab2ba2b2ab3abb2a2b3ab3a2a3
b2b2ab2b3a2b2ab3a3b2a2b3aba2aba2b
a3a3aba2abb2a3a2bab2b3a2b2ab3a2b3
a2ba2bba2b2abb2a2b3a2bab2b3a2ab3a3a
ab2ab2a2b2ab3b2a2b3aab2b3a2aba3a2bb
b3b3ab3a3a2b3abb3a2abb2a2bab2a2b2
a2b2a2b2b2a2b3ab2b3a2a2b2ab3a3a2babab
ab3ab3a2b3ab3a2abab3a3a2bab2ba2b2b2
a2b3a2b3b3a2ab3a3a2ba2b3aba2b2abb2ab2

Right Cayley graph

Idempotents are shown in bold.

Others with same cardinality

26 unique, 301 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
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.

2 total

Σ#PresentationMapping
1114655⟨a, b | aaba=b, bbabb=a⟩φ(a) = a, φ(b) = b
1114659⟨a, b | aaba=b, bbbab=a⟩φ(a) = a, φ(b) = b