#4643 ⟨a, b | aaaa=b, abbb=b⟩

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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. a13 ⇒ a4
  2. b ⇒ a4 
# ab:aaaa=b,abbb=b a/b
aaaaaaaaaaaaa=aaaa
b=aaaa

Staircase diagram

Cayley table

Idempotents are shown in bold.

1aa2a3a4a5a6a7a8a9a10a11a12
11aa2a3a4a5a6a7a8a9a10a11a12
aaa2a3a4a5a6a7a8a9a10a11a12a4
a2a2a3a4a5a6a7a8a9a10a11a12a4a5
a3a3a4a5a6a7a8a9a10a11a12a4a5a6
a4a4a5a6a7a8a9a10a11a12a4a5a6a7
a5a5a6a7a8a9a10a11a12a4a5a6a7a8
a6a6a7a8a9a10a11a12a4a5a6a7a8a9
a7a7a8a9a10a11a12a4a5a6a7a8a9a10
a8a8a9a10a11a12a4a5a6a7a8a9a10a11
a9a9a10a11a12a4a5a6a7a8a9a10a11a12
a10a10a11a12a4a5a6a7a8a9a10a11a12a4
a11a11a12a4a5a6a7a8a9a10a11a12a4a5
a12a12a4a5a6a7a8a9a10a11a12a4a5a6

Right Cayley graph

Idempotents are shown in bold.

Others with same cardinality

26 unique, 297 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
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
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.

6 total

Σ#PresentationMapping
104647⟨a, b | aaaa=b, babb=b⟩φ(a) = a, φ(b) = aaaa
1119353⟨a, b | aaa=b, abbbb=ab⟩φ(a) = a, φ(b) = aaa
1119354⟨a, b | aaa=b, abbbb=ba⟩φ(a) = a, φ(b) = aaa
1119367⟨a, b | aaa=b, babbb=ab⟩φ(a) = a, φ(b) = aaa
1119368⟨a, b | aaa=b, babbb=ba⟩φ(a) = a, φ(b) = aaa
1119371⟨a, b | aaa=b, bbabb=ab⟩φ(a) = a, φ(b) = aaa