#6633 ⟨a, b | aab=a, baaa=bb⟩

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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. a5 ⇒ a
  2. ab ⇒ a4
  3. b2 ⇒ ba3 
# ab:aab=a,baaa=bb a/b
aaaaa=a
ab=aaaa
bb=baaa

Cayley table

Idempotents are shown in bold.

1aba2baa3ba2a4ba3ba4
11aba2baa3ba2a4ba3ba4
aaa2a4a3aa4a2aa3a4
bbbaba3ba2ba4ba3baba4ba2ba3
a2a2a3aa4a2aa3a2a4a
bababa2ba4ba3baba4ba2baba3ba4
a3a3a4a2aa3a2a4a3aa2
ba2ba2ba3baba4ba2baba3ba2ba4ba
a4a4aa3a2a4a3aa4a2a3
ba3ba3ba4ba2baba3ba2ba4ba3baba2
ba4ba4baba3ba2ba4ba3baba4ba2ba3

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

31 unique, 898 total

Σ#PresentationDescriptionRelated
7332⟨a, b | aa=1, abbb=b⟩Finite non-commutative monoid with 10 elements51 iso, 34 anti-iso
8507⟨a, b | aaa=b, abbb=1⟩Isomorphic to ℤ10536 iso
8656⟨a, b | bb=aa, aba=a⟩Finite non-commutative monoid with 10 elements1 iso
8657⟨a, b | bb=aa, aba=b⟩Finite non-commutative monoid with 10 elements1 iso
8970⟨a, b | aa=a, bbb=ab⟩Finite non-commutative monoid with 10 elements3 iso
91654⟨a, b | aab=bb, bba=a⟩Finite non-commutative monoid with 10 elements6 iso
92012⟨a, b | aaa=b, abbb=a⟩Isomorphic to ℕ(10 = 1)59 iso
92013⟨a, b | aaa=b, abbb=b⟩Isomorphic to ℕ(10 = 3)35 iso
92277⟨a, b | bb=aa, aba=aa⟩Finite non-commutative monoid with 10 elements1 iso
92894⟨a, b | aa=a, bbbbb=a⟩Isomorphic to ℕ(10 = 5)17 iso
92935⟨a, b | aa=b, bbbbb=b⟩Isomorphic to ℕ(10 = 2)57 iso
104637⟨a, b | aaaa=b, aabb=b⟩Isomorphic to ℕ(10 = 4)20 iso
105346⟨a, b | aaa=bb, abb=ab⟩Finite non-commutative monoid with 10 elements2 iso, 1 anti-iso
105356⟨a, b | aab=aa, aba=bb⟩Finite non-commutative monoid with 10 elements
106587⟨a, b | aaa=b, abbb=bb⟩Isomorphic to ℕ(10 = 6)3 iso
107089⟨a, b | ab=aa, baaa=bb⟩Finite non-commutative monoid with 10 elements3 iso
108619⟨a, b | aa=a, abbbbb=b⟩Finite non-commutative monoid with 10 elements5 iso
109051⟨a, b | ab=a, baaaa=bb⟩Finite non-commutative monoid with 10 elements4 iso
1110729⟨a, b | aaab=baa, abab=1⟩Finite non-Abelian group with 10 elements3 iso
1112157⟨a, b | aaaa=aa, abba=b⟩Finite non-commutative monoid with 10 elements
1112181⟨a, b | aaaa=ab, baaa=b⟩Finite non-commutative monoid with 10 elements1 iso
1112196⟨a, b | aaaa=bb, aaab=a⟩Finite commutative monoid with 10 elements7 iso
1112197⟨a, b | aaaa=bb, aaab=b⟩Finite commutative monoid with 10 elements1 iso
1112452⟨a, b | aabb=aa, bbbb=a⟩Isomorphic to ℕ(10 = 8)3 iso
1115738⟨a, b | aab=bb, aaaaa=b⟩Isomorphic to ℕ(10 = 7)7 iso
1119564⟨a, b | aab=b, abbbb=aa⟩Finite commutative monoid with 10 elements5 iso
1119899⟨a, b | aaa=b, abbb=bbb⟩Isomorphic to ℕ(10 = 9)1 iso
1120052⟨a, b | aab=b, aaaa=baa⟩Finite non-commutative monoid with 10 elements
1120253⟨a, b | aba=b, aaaa=bbb⟩Finite commutative monoid with 10 elements
1125905⟨a, b | ab=a, bbbb=baaa⟩Finite non-commutative monoid with 10 elements
1125909⟨a, b | ab=a, bbbb=bbaa⟩Finite non-commutative monoid with 10 elements

Other isomorphic instances

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

20 total

Σ#PresentationMapping
106983⟨a, b | ab=aa, baaaa=b⟩φ(a) = b, φ(b) = aaa
106985⟨a, b | ab=aa, baaab=b⟩φ(a) = b, φ(b) = aaa
106987⟨a, b | ab=aa, baaba=b⟩φ(a) = b, φ(b) = aaa
106989⟨a, b | ab=aa, baabb=b⟩φ(a) = b, φ(b) = aaa
106991⟨a, b | ab=aa, babaa=b⟩φ(a) = b, φ(b) = aaa
106993⟨a, b | ab=aa, babab=b⟩φ(a) = b, φ(b) = aaa
106995⟨a, b | ab=aa, babba=b⟩φ(a) = b, φ(b) = aaa
106997⟨a, b | ab=aa, babbb=b⟩φ(a) = b, φ(b) = aaa
106999⟨a, b | ab=aa, bbaaa=b⟩φ(a) = b, φ(b) = aaa
107001⟨a, b | ab=aa, bbaab=b⟩φ(a) = b, φ(b) = aaa
107003⟨a, b | ab=aa, bbaba=b⟩φ(a) = b, φ(b) = aaa
107005⟨a, b | ab=aa, bbabb=b⟩φ(a) = b, φ(b) = aaa
107007⟨a, b | ab=aa, bbbaa=b⟩φ(a) = b, φ(b) = aaa
107009⟨a, b | ab=aa, bbbab=b⟩φ(a) = b, φ(b) = aaa
107011⟨a, b | ab=aa, bbbba=b⟩φ(a) = b, φ(b) = aaa
1112505⟨a, b | abab=aa, baab=b⟩φ(a) = b, φ(b) = aa
1112507⟨a, b | abab=aa, baba=b⟩φ(a) = b, φ(b) = aa
1112511⟨a, b | abab=aa, bbaa=b⟩φ(a) = b, φ(b) = aa
1112561⟨a, b | abba=aa, baba=b⟩φ(a) = b, φ(b) = aa
1112565⟨a, b | abba=aa, bbaa=b⟩φ(a) = b, φ(b) = aa

Other anti-isomorphic instances

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

1 total

Σ#PresentationMapping
1115804⟨a, b | aba=aa, aaaab=b⟩φ(a) = b, φ(b) = aaaa