#12268 ⟨a, b | aaab=ab, bbbb=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. b13 ⇒ b5
  2. a ⇒ b4 
# ab:aaab=ab,bbbb=a b/a
bbbbbbbbbbbbb=bbbbb
a=bbbb

Staircase diagram

Cayley table

Idempotents are shown in bold.

1bb2b3b4b5b6b7b8b9b10b11b12
11bb2b3b4b5b6b7b8b9b10b11b12
bbb2b3b4b5b6b7b8b9b10b11b12b5
b2b2b3b4b5b6b7b8b9b10b11b12b5b6
b3b3b4b5b6b7b8b9b10b11b12b5b6b7
b4b4b5b6b7b8b9b10b11b12b5b6b7b8
b5b5b6b7b8b9b10b11b12b5b6b7b8b9
b6b6b7b8b9b10b11b12b5b6b7b8b9b10
b7b7b8b9b10b11b12b5b6b7b8b9b10b11
b8b8b9b10b11b12b5b6b7b8b9b10b11b12
b9b9b10b11b12b5b6b7b8b9b10b11b12b5
b10b10b11b12b5b6b7b8b9b10b11b12b5b6
b11b11b12b5b6b7b8b9b10b11b12b5b6b7
b12b12b5b6b7b8b9b10b11b12b5b6b7b8

Right Cayley graph

Idempotents are shown in bold.

Others with same cardinality

26 unique, 300 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
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.

3 total

Σ#PresentationMapping
1112296⟨a, b | aaab=ba, bbbb=a⟩φ(a) = bbbb, φ(b) = b
1112376⟨a, b | aaba=ab, bbbb=a⟩φ(a) = bbbb, φ(b) = b
1112402⟨a, b | aaba=ba, bbbb=a⟩φ(a) = bbbb, φ(b) = b