#16293 ⟨a, b | aab=bb, abab=aa⟩

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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 ⇒ a3
  2. ba3 ⇒ a5
  3. aba2 ⇒ a5
  4. a2b ⇒ a4
  5. b2 ⇒ a4
  6. (ab)2 ⇒ a2 
# ab:aab=bb,abab=aa a/b
aaaaaaa=aaa
baaa=aaaaa
abaa=aaaaa
aab=aaaa
bb=aaaa
abab=aa

Cayley table

Idempotents are shown in bold.

1aba2abbaa3ababa2baba4(ba)2a5a6
11aba2abbaa3ababa2baba4(ba)2a5a6
aaa2aba3a4abaa4a5a5a2a5a3a6a3
bbbaa4ba2baba5a5(ba)2a6a3a6a4a3a4
a2a2a3a4a4a5a5a5a6a6a3a6a4a3a4
abababaa5a5a2a6a6a3a3a4a3a5a4a5
bababa2baba5a6(ba)2a6a3a3ba2a3a5a4a5
a3a3a4a5a5a6a6a6a3a3a4a3a5a4a5
abaabaa5a2a6a3a3a3a4a4a5a4a6a5a6
ba2ba2a5a6a6a3a3a3a4a4a5a4a6a5a6
babbab(ba)2a3a3ba2a4a4a5a5a6a5a3a6a3
a4a4a5a6a6a3a3a3a4a4a5a4a6a5a6
(ba)2(ba)2a3ba2a4a5a5a5a6a6a3a6a4a3a4
a5a5a6a3a3a4a4a4a5a5a6a5a3a6a3
a6a6a3a4a4a5a5a5a6a6a3a6a4a3a4

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

30 unique, 316 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
1114384⟨a, b | aaaa=b, aabbb=b⟩Isomorphic to ℕ(14 = 4)5 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
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