#1963 ⟨a, b | aba=b, aaabb=1⟩

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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. a6 ⇒ 1
  2. ab ⇒ ba5
  3. b2 ⇒ a3 
# ab:aba=b,aaabb=1 a/b
aaaaaa=1
ab=baaaaa
bb=aaa

Cayley table

1aba2baa3ba2a4ba3a5ba4ba5
11aba2baa3ba2a4ba3a5ba4ba5
aaa2ba5a3ba4baa5ba21ba3ba4
bbbaa3ba2a4ba3a5ba41ba5aa2
a2a2a3ba4a4ba5a5b1baaba2ba3
bababa2a2ba3a3ba4a4ba5a5b1a
a3a3a4ba3a5ba41ba5aba2baba2
ba2ba2ba3aba4a2ba5a3ba4baa51
a4a4a5ba21ba3aba4a2ba5a3bba
ba3ba3ba41ba5aba2baa3ba2a4a5
a5a51baaba2a2ba3a3ba4a4ba5b
ba4ba4ba5a5b1baaba2a2ba3a3a4
ba5ba5ba4baa5ba21ba3aba4a2a3

Right Cayley graph

Left Cayley graph

Others with same cardinality

37 unique, 629 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
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
1121086⟨a, b | bb=aa, aaaa=aba⟩Finite non-commutative monoid with 12 elements4 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.

30 total

Σ#PresentationMapping
91966⟨a, b | aba=b, aabba=1⟩φ(a) = a, φ(b) = b
91974⟨a, b | aba=b, baaab=1⟩φ(a) = a, φ(b) = b
104111⟨a, b | bab=aba, aabb=1⟩φ(a) = b, φ(b) = baa
104113⟨a, b | bab=aba, abba=1⟩φ(a) = b, φ(b) = baa
104601⟨a, b | abba=b, aabbb=1⟩φ(a) = b, φ(b) = a
104606⟨a, b | abba=b, abbba=1⟩φ(a) = b, φ(b) = a
104609⟨a, b | abba=b, baabb=1⟩φ(a) = b, φ(b) = a
105881⟨a, b | aabb=1, ababa=b⟩φ(a) = b, φ(b) = baa
105945⟨a, b | abba=1, ababa=b⟩φ(a) = b, φ(b) = baa
105958⟨a, b | abba=1, babab=a⟩φ(a) = b, φ(b) = baa
1111855⟨a, b | aaba=ab, aaabb=1⟩φ(a) = a, φ(b) = b
1111858⟨a, b | aaba=ab, aabba=1⟩φ(a) = a, φ(b) = b
1111864⟨a, b | aaba=ab, abbaa=1⟩φ(a) = a, φ(b) = b
1111869⟨a, b | aaba=ab, baaab=1⟩φ(a) = a, φ(b) = b
1111876⟨a, b | aaba=ab, bbaaa=1⟩φ(a) = a, φ(b) = b
1112019⟨a, b | abab=aa, aabbb=1⟩φ(a) = b, φ(b) = a
1112026⟨a, b | abab=aa, abbba=1⟩φ(a) = b, φ(b) = a
1112031⟨a, b | abab=aa, baabb=1⟩φ(a) = b, φ(b) = a
1112037⟨a, b | abab=aa, bbaab=1⟩φ(a) = b, φ(b) = a
1112040⟨a, b | abab=aa, bbbaa=1⟩φ(a) = b, φ(b) = a
1115160⟨a, b | aab=ba, ababbb=1⟩φ(a) = aa, φ(b) = b
1115166⟨a, b | aab=ba, abbbab=1⟩φ(a) = aa, φ(b) = b
1115180⟨a, b | aab=ba, bababb=1⟩φ(a) = aa, φ(b) = b
1115183⟨a, b | aab=ba, babbba=1⟩φ(a) = aa, φ(b) = b
1115190⟨a, b | aab=ba, bbabab=1⟩φ(a) = aa, φ(b) = b
1115195⟨a, b | aab=ba, bbbaba=1⟩φ(a) = aa, φ(b) = b
1118621⟨a, b | aba=b, aaaabab=1⟩φ(a) = a, φ(b) = b
1118626⟨a, b | aba=b, aaababa=1⟩φ(a) = a, φ(b) = b
1118635⟨a, b | aba=b, aababaa=1⟩φ(a) = a, φ(b) = b
1118646⟨a, b | aba=b, abaaaab=1⟩φ(a) = a, φ(b) = b