#20168 ⟨a, b | aab=b, bbbb=aaa⟩

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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. b9 ⇒ b
  2. ab ⇒ b5
  3. ba ⇒ b5
  4. a3 ⇒ b4 
# ab:aab=b,bbbb=aaa b/a
bbbbbbbbb=b
ab=bbbbb
ba=bbbbb
aaa=bbbb

Staircase diagram

Cayley table

Idempotents are shown in bold.

1aba2b2b3b4b5b6b7b8
11aba2b2b3b4b5b6b7b8
aaa2b5b4b6b7b8bb2b3b4
bbb5b2bb3b4b5b6b7b8b
a2a2b4bb8b2b3b4b5b6b7b8
b2b2b6b3b2b4b5b6b7b8bb2
b3b3b7b4b3b5b6b7b8bb2b3
b4b4b8b5b4b6b7b8bb2b3b4
b5b5bb6b5b7b8bb2b3b4b5
b6b6b2b7b6b8bb2b3b4b5b6
b7b7b3b8b7bb2b3b4b5b6b7
b8b8b4bb8b2b3b4b5b6b7b8

Right Cayley graph

Idempotents are shown in bold.

Others with same cardinality

29 unique, 480 total

Σ#PresentationDescriptionRelated
91472⟨a, b | aaa=bb, abbb=1⟩Isomorphic to ℤ11259 iso
104155⟨a, b | abb=aaa, bba=b⟩Finite non-commutative monoid with 11 elements4 iso
105086⟨a, b | aaa=bb, abbb=a⟩Finite commutative monoid with 11 elements11 iso
105087⟨a, b | aaa=bb, abbb=b⟩Finite commutative monoid with 11 elements3 iso
105111⟨a, b | aab=aa, baaa=b⟩Finite non-commutative monoid with 11 elements7 iso
105322⟨a, b | aaa=ab, abb=bb⟩Finite non-commutative monoid with 11 elements3 iso
105335⟨a, b | aaa=ab, bbb=aa⟩Finite non-commutative monoid with 11 elements2 iso, 1 anti-iso
105410⟨a, b | aab=bb, bab=aa⟩Finite non-commutative monoid with 11 elements2 iso
106292⟨a, b | aaa=b, aabbb=a⟩Isomorphic to ℕ(11 = 1)35 iso
106293⟨a, b | aaa=b, aabbb=b⟩Isomorphic to ℕ(11 = 3)11 iso
106380⟨a, b | aab=a, bbbbb=a⟩Isomorphic to ℕ(11 = 5)1 iso
106834⟨a, b | aba=b, abb=aaa⟩Finite non-commutative monoid with 11 elements
107114⟨a, b | ab=aa, bbbb=aa⟩Finite non-commutative monoid with 11 elements1 iso
107116⟨a, b | ab=aa, bbbb=ba⟩Finite non-commutative monoid with 11 elements
108691⟨a, b | aa=b, abbbbb=b⟩Isomorphic to ℕ(11 = 2)32 iso
108777⟨a, b | ab=a, baaaaa=b⟩Finite non-commutative monoid with 11 elements20 iso, 5 anti-iso
109083⟨a, b | ab=a, bbaaa=bb⟩Finite non-commutative monoid with 11 elements4 iso
1112179⟨a, b | aaaa=ab, abbb=b⟩Isomorphic to ℕ(11 = 4)20 iso
1115607⟨a, b | aab=aa, bbbbb=a⟩Isomorphic to ℕ(11 = 10)1 iso
1115671⟨a, b | aab=ab, bbbbb=a⟩Isomorphic to ℕ(11 = 6)8 iso
1116148⟨a, b | aab=ab, aaaa=bb⟩Finite non-commutative monoid with 11 elements1 iso
1116212⟨a, b | aab=ba, aaaa=bb⟩Finite non-commutative monoid with 11 elements
1118715⟨a, b | aaa=a, aabbba=b⟩Finite non-commutative monoid with 11 elements
1119070⟨a, b | aab=b, bbabbb=a⟩Finite commutative monoid with 11 elements4 iso
1120096⟨a, b | aab=b, abba=aaa⟩Finite non-commutative monoid with 11 elements1 iso
1120112⟨a, b | aab=b, baaa=aaa⟩Finite non-commutative monoid with 11 elements
1120885⟨a, b | bb=aa, aaaaa=ab⟩Finite non-commutative monoid with 11 elements7 iso, 8 anti-iso
1125539⟨a, b | ab=a, baaaa=bbb⟩Finite non-commutative monoid with 11 elements
1125635⟨a, b | ab=a, bbbaa=bbb⟩Finite non-commutative monoid with 11 elements