#14384 ⟨a, b | aaaa=b, aabbb=b⟩

Up:Monoids with two generators and two relations
Prev:#14383 ⟨a, b | aaaa=b, aabbb=a⟩
Next:#14395 ⟨a, b | aaaa=b, abbbb=a⟩

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. a14 ⇒ a4
  2. b ⇒ a4 
# ab:aaaa=b,aabbb=b a/b
aaaaaaaaaaaaaa=aaaa
b=aaaa

Staircase diagram

Cayley table

Idempotents are shown in bold.

1aa2a3a4a5a6a7a8a9a10a11a12a13
11aa2a3a4a5a6a7a8a9a10a11a12a13
aaa2a3a4a5a6a7a8a9a10a11a12a13a4
a2a2a3a4a5a6a7a8a9a10a11a12a13a4a5
a3a3a4a5a6a7a8a9a10a11a12a13a4a5a6
a4a4a5a6a7a8a9a10a11a12a13a4a5a6a7
a5a5a6a7a8a9a10a11a12a13a4a5a6a7a8
a6a6a7a8a9a10a11a12a13a4a5a6a7a8a9
a7a7a8a9a10a11a12a13a4a5a6a7a8a9a10
a8a8a9a10a11a12a13a4a5a6a7a8a9a10a11
a9a9a10a11a12a13a4a5a6a7a8a9a10a11a12
a10a10a11a12a13a4a5a6a7a8a9a10a11a12a13
a11a11a12a13a4a5a6a7a8a9a10a11a12a13a4
a12a12a13a4a5a6a7a8a9a10a11a12a13a4a5
a13a13a4a5a6a7a8a9a10a11a12a13a4a5a6

Right Cayley graph

Idempotents are shown in bold.

Others with same cardinality

30 unique, 311 total

Σ#PresentationDescriptionRelated
81123⟨a, b | aa=1, abbbb=b⟩Finite non-commutative monoid with 14 elements42 iso, 17 anti-iso
91682⟨a, b | aba=bb, bab=a⟩Finite non-commutative monoid with 14 elements1 iso
93034⟨a, b | aa=a, bbbb=ab⟩Finite non-commutative monoid with 14 elements2 iso
103773⟨a, b | aaaa=bb, abbb=1⟩Isomorphic to ℤ14165 iso
105218⟨a, b | aab=bb, bbba=a⟩Finite non-commutative monoid with 14 elements5 iso, 1 anti-iso
105404⟨a, b | aab=bb, aba=aa⟩Finite non-commutative monoid with 14 elements1 iso
106718⟨a, b | aab=b, bbba=aa⟩Finite non-commutative monoid with 14 elements2 iso
1112183⟨a, b | aaaa=ab, baab=b⟩Finite non-commutative monoid with 14 elements3 iso
1112206⟨a, b | aaaa=bb, abbb=a⟩Finite commutative monoid with 14 elements1 iso
1112207⟨a, b | aaaa=bb, abbb=b⟩Finite commutative monoid with 14 elements1 iso
1112441⟨a, b | aabb=aa, baab=b⟩Finite non-commutative monoid with 14 elements3 iso
1112499⟨a, b | abab=aa, abba=b⟩Finite non-commutative monoid with 14 elements
1114383⟨a, b | aaaa=b, aabbb=a⟩Isomorphic to ℕ(14 = 1)15 iso
1115532⟨a, b | aaa=bb, abbbb=b⟩Isomorphic to ℕ(14 = 3)11 iso
1115539⟨a, b | aaa=bb, babbb=a⟩Finite commutative monoid with 14 elements
1116020⟨a, b | aaa=ab, baab=bb⟩Finite non-commutative monoid with 14 elements1 iso
1116079⟨a, b | aaa=bb, bbbb=ab⟩Finite non-commutative monoid with 14 elements
1116293⟨a, b | aab=bb, abab=aa⟩Finite non-commutative monoid with 14 elements
1116470⟨a, b | aba=bb, bbbb=aa⟩Finite non-commutative monoid with 14 elements
1119552⟨a, b | aab=b, abbaa=aa⟩Finite non-commutative monoid with 14 elements2 iso
1120844⟨a, b | ab=aa, bbbbb=aa⟩Finite non-commutative monoid with 14 elements1 iso
1120846⟨a, b | ab=aa, bbbbb=ba⟩Finite non-commutative monoid with 14 elements
1121023⟨a, b | ab=aa, bbaa=bbb⟩Finite non-commutative monoid with 14 elements1 iso
1121040⟨a, b | ab=aa, bbbb=aaa⟩Finite non-commutative monoid with 14 elements3 iso
1121044⟨a, b | ab=aa, bbbb=baa⟩Finite non-commutative monoid with 14 elements1 iso
1121046⟨a, b | ab=aa, bbbb=bba⟩Finite non-commutative monoid with 14 elements
1121110⟨a, b | bb=aa, abab=aaa⟩Finite non-commutative monoid with 14 elements2 anti-iso
1124186⟨a, b | aa=a, bbbbbbb=a⟩Isomorphic to ℕ(14 = 7)
1124331⟨a, b | aa=b, bbbbbbb=b⟩Isomorphic to ℕ(14 = 2)
1125055⟨a, b | ab=a, bbaaaa=bb⟩Finite non-commutative monoid with 14 elements

Other isomorphic instances

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

5 total

Σ#PresentationMapping
1114390⟨a, b | aaaa=b, ababb=b⟩φ(a) = a, φ(b) = aaaa
1114392⟨a, b | aaaa=b, abbab=b⟩φ(a) = a, φ(b) = aaaa
1114394⟨a, b | aaaa=b, abbba=b⟩φ(a) = a, φ(b) = aaaa
1114400⟨a, b | aaaa=b, baabb=b⟩φ(a) = a, φ(b) = aaaa
1114402⟨a, b | aaaa=b, babab=b⟩φ(a) = a, φ(b) = aaaa