#21086 ⟨a, b | bb=aa, aaaa=aba⟩

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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. a7 ⇒ a5
  2. ba3 ⇒ a5
  3. aba ⇒ a4
  4. a2b ⇒ ba2
  5. b2 ⇒ a2 
# ab:bb=aa,aaaa=aba a/b
aaaaaaa=aaaaa
baaa=aaaaa
aba=aaaa
aab=baa
bb=aa

Cayley table

Idempotents are shown in bold.

1aba2abbaa3ba2baba4a5a6
11aba2abbaa3ba2baba4a5a6
aaa2aba3ba2a4a4a5a6a5a6a5
bbbaa2ba2baba3a5a4a5a6a5a6
a2a2a3ba2a4a5a5a5a6a5a6a5a6
ababa4a3a5a6a4a6a5a6a5a6a5
bababa2baba5a4a6a6a5a6a5a6a5
a3a3a4a5a5a6a6a6a5a6a5a6a5
ba2ba2a5a4a6a5a5a5a6a5a6a5a6
babbaba6a5a5a6a6a6a5a6a5a6a5
a4a4a5a6a6a5a5a5a6a5a6a5a6
a5a5a6a5a5a6a6a6a5a6a5a6a5
a6a6a5a6a6a5a5a5a6a5a6a5a6

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

37 unique, 655 total

Σ#PresentationDescriptionRelated
7124⟨a, b | aab=a, bbb=1⟩Finite non-commutative monoid with 12 elements23 iso, 38 anti-iso
8458⟨a, b | aaaa=1, abbb=1⟩Isomorphic to ℤ12325 iso
8645⟨a, b | ab=aa, bbb=b⟩Finite non-commutative monoid with 12 elements1 anti-iso
91646⟨a, b | aab=bb, aba=a⟩Finite non-commutative monoid with 12 elements2 iso
91963⟨a, b | aba=b, aaabb=1⟩Finite non-Abelian group with 12 elements30 iso
91998⟨a, b | aaa=a, bbbb=a⟩Isomorphic to ℕ(12 = 4)6 iso
92018⟨a, b | aaa=b, bbbb=a⟩Isomorphic to ℕ(12 = 1)27 iso
92019⟨a, b | aaa=b, bbbb=b⟩Isomorphic to ℕ(12 = 3)23 iso
92259⟨a, b | ab=aa, bbb=bb⟩Finite non-commutative monoid with 12 elements
105040⟨a, b | aaa=aa, bbbb=a⟩Isomorphic to ℕ(12 = 8)
105072⟨a, b | aaa=ab, bbbb=a⟩Isomorphic to ℕ(12 = 5)7 iso
105092⟨a, b | aaa=bb, bbbb=a⟩Isomorphic to ℕ(12 = 2)43 iso
105202⟨a, b | aab=bb, abba=a⟩Finite non-commutative monoid with 12 elements9 iso, 32 anti-iso
105330⟨a, b | aaa=ab, bab=bb⟩Finite non-commutative monoid with 12 elements1 iso
106597⟨a, b | aaa=b, bbbb=bb⟩Isomorphic to ℕ(12 = 6)4 iso
106660⟨a, b | aab=a, bbbb=ba⟩Finite non-commutative monoid with 12 elements1 anti-iso
106661⟨a, b | aab=a, bbbb=bb⟩Finite non-commutative monoid with 12 elements1 anti-iso
107105⟨a, b | ab=aa, bbaa=bb⟩Finite non-commutative monoid with 12 elements2 iso
1112897⟨a, b | aab=aaa, baaa=b⟩Finite non-commutative monoid with 12 elements5 iso
1112910⟨a, b | aab=aaa, bbbb=a⟩Isomorphic to ℕ(12 = 9)2 iso
1115428⟨a, b | aaa=aa, abbbb=b⟩Finite non-commutative monoid with 12 elements
1115996⟨a, b | aaa=ab, aabb=bb⟩Finite non-commutative monoid with 12 elements2 iso
1116057⟨a, b | aaa=bb, aabb=ab⟩Finite non-commutative monoid with 12 elements2 iso, 2 anti-iso
1116104⟨a, b | aab=aa, abab=bb⟩Finite non-commutative monoid with 12 elements
1116274⟨a, b | aab=bb, aaaa=ab⟩Finite non-commutative monoid with 12 elements1 iso
1116275⟨a, b | aab=bb, aaaa=ba⟩Finite non-commutative monoid with 12 elements
1116448⟨a, b | aba=bb, aabb=aa⟩Finite non-commutative monoid with 12 elements2 iso
1119773⟨a, b | aba=b, bbbbb=aa⟩Finite commutative monoid with 12 elements
1119917⟨a, b | aaa=b, bbbb=abb⟩Isomorphic to ℕ(12 = 7)2 iso
1120054⟨a, b | aab=b, aaaa=bba⟩Finite non-commutative monoid with 12 elements
1120686⟨a, b | bb=aa, aaaaab=a⟩Finite commutative monoid with 12 elements15 iso
1120787⟨a, b | ab=aa, baaaa=bb⟩Finite non-commutative monoid with 12 elements7 iso
1121092⟨a, b | bb=aa, aaab=aba⟩Finite non-commutative monoid with 12 elements3 iso
1121112⟨a, b | bb=aa, abab=aba⟩Finite non-commutative monoid with 12 elements
1124147⟨a, b | aa=a, abbbbbb=b⟩Finite non-commutative monoid with 12 elements
1124991⟨a, b | ab=a, baaaaa=bb⟩Finite non-commutative monoid with 12 elements
1125603⟨a, b | ab=a, bbaaa=bbb⟩Finite non-commutative monoid with 12 elements

Other isomorphic instances

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

4 total

Σ#PresentationMapping
1121088⟨a, b | bb=aa, aaaa=bab⟩φ(a) = b, φ(b) = a
1121108⟨a, b | bb=aa, aabb=aba⟩φ(a) = a, φ(b) = b
1121116⟨a, b | bb=aa, abba=aba⟩φ(a) = a, φ(b) = b
1121118⟨a, b | bb=aa, abba=bab⟩φ(a) = b, φ(b) = a