#4212 ⟨a, b | aaaaa=1, abbbb=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. b20 ⇒ 1
  2. a ⇒ b16 
# ab:aaaaa=1,abbbb=1 b/a
bbbbbbbbbbbbbbbbbbbb=1
a=bbbbbbbbbbbbbbbb

Staircase diagram

Cayley table

1bb2b3b4b5b6b7b8b9b10b11b12b13b14b15b16b17b18b19
11bb2b3b4b5b6b7b8b9b10b11b12b13b14b15b16b17b18b19
bbb2b3b4b5b6b7b8b9b10b11b12b13b14b15b16b17b18b191
b2b2b3b4b5b6b7b8b9b10b11b12b13b14b15b16b17b18b191b
b3b3b4b5b6b7b8b9b10b11b12b13b14b15b16b17b18b191bb2
b4b4b5b6b7b8b9b10b11b12b13b14b15b16b17b18b191bb2b3
b5b5b6b7b8b9b10b11b12b13b14b15b16b17b18b191bb2b3b4
b6b6b7b8b9b10b11b12b13b14b15b16b17b18b191bb2b3b4b5
b7b7b8b9b10b11b12b13b14b15b16b17b18b191bb2b3b4b5b6
b8b8b9b10b11b12b13b14b15b16b17b18b191bb2b3b4b5b6b7
b9b9b10b11b12b13b14b15b16b17b18b191bb2b3b4b5b6b7b8
b10b10b11b12b13b14b15b16b17b18b191bb2b3b4b5b6b7b8b9
b11b11b12b13b14b15b16b17b18b191bb2b3b4b5b6b7b8b9b10
b12b12b13b14b15b16b17b18b191bb2b3b4b5b6b7b8b9b10b11
b13b13b14b15b16b17b18b191bb2b3b4b5b6b7b8b9b10b11b12
b14b14b15b16b17b18b191bb2b3b4b5b6b7b8b9b10b11b12b13
b15b15b16b17b18b191bb2b3b4b5b6b7b8b9b10b11b12b13b14
b16b16b17b18b191bb2b3b4b5b6b7b8b9b10b11b12b13b14b15
b17b17b18b191bb2b3b4b5b6b7b8b9b10b11b12b13b14b15b16
b18b18b191bb2b3b4b5b6b7b8b9b10b11b12b13b14b15b16b17
b19b191bb2b3b4b5b6b7b8b9b10b11b12b13b14b15b16b17b18

Right Cayley graph

Others with same cardinality

20 unique, 49 total

Σ#PresentationDescriptionRelated
8526⟨a, b | aab=a, bbbb=1⟩Finite non-commutative monoid with 20 elements10 iso, 9 anti-iso
92207⟨a, b | ab=aa, bbbb=b⟩Finite non-commutative monoid with 20 elements1 anti-iso
104095⟨a, b | baa=abb, abab=1⟩Finite non-Abelian group with 20 elements4 iso, 1 anti-iso
105349⟨a, b | aaa=bb, bab=aa⟩Finite non-commutative monoid with 20 elements1 iso
106728⟨a, b | aba=a, aaaa=bb⟩Finite non-commutative monoid with 20 elements
106764⟨a, b | aba=b, aaaa=bb⟩Finite non-commutative monoid with 20 elements
107117⟨a, b | ab=aa, bbbb=bb⟩Finite non-commutative monoid with 20 elements
1112159⟨a, b | aaaa=aa, abbb=b⟩Finite non-commutative monoid with 20 elements
1112322⟨a, b | aaab=bb, bbba=a⟩Finite non-commutative monoid with 20 elements
1114367⟨a, b | aaaa=a, bbbbb=a⟩Isomorphic to ℕ(20 = 5)
1114407⟨a, b | aaaa=b, bbbbb=a⟩Isomorphic to ℕ(20 = 1)
1114408⟨a, b | aaaa=b, bbbbb=b⟩Isomorphic to ℕ(20 = 4)
1115933⟨a, b | aba=bb, baaab=a⟩Finite non-commutative monoid with 20 elements
1116124⟨a, b | aab=aa, baba=bb⟩Finite non-commutative monoid with 20 elements
1116339⟨a, b | aba=aa, aaaa=bb⟩Finite non-commutative monoid with 20 elements
1116343⟨a, b | aba=aa, aaab=bb⟩Finite non-commutative monoid with 20 elements
1116545⟨a, b | aba=bb, abb=aaa⟩Finite non-commutative monoid with 20 elements
1118619⟨a, b | aba=b, aaaaabb=1⟩Finite non-Abelian group with 20 elements3 iso
1119503⟨a, b | aab=a, bbbbb=bb⟩Finite non-commutative monoid with 20 elements
1121047⟨a, b | ab=aa, bbbb=bbb⟩Finite non-commutative monoid with 20 elements

Other isomorphic instances

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

16 total

Σ#PresentationMapping
104216⟨a, b | aaaaa=1, babbb=1⟩φ(a) = bbbbbbbbbbbbbbbb, φ(b) = b
104217⟨a, b | aaaaa=1, bbabb=1⟩φ(a) = bbbbbbbbbbbbbbbb, φ(b) = b
104381⟨a, b | aaaa=b, bbbbb=1⟩φ(a) = b, φ(b) = bbbb
105447⟨a, b | aaaa=1, abbbbb=1⟩φ(a) = bbbbbbbbbbbbbbb, φ(b) = b
105454⟨a, b | aaaa=1, babbbb=1⟩φ(a) = bbbbbbbbbbbbbbb, φ(b) = b
105456⟨a, b | aaaa=1, bbabbb=1⟩φ(a) = bbbbbbbbbbbbbbb, φ(b) = b
105732⟨a, b | aaaa=1, bbbbb=a⟩φ(a) = bbbbb, φ(b) = b
1111691⟨a, b | aaaa=bb, bbbbb=1⟩φ(a) = b, φ(b) = bbbbbbbbbbbb
1113287⟨a, b | aaaaa=1, aabbbb=1⟩φ(a) = bbbbbbbb, φ(b) = b
1113297⟨a, b | aaaaa=1, abbbba=1⟩φ(a) = bbbbbbbb, φ(b) = b
1113302⟨a, b | aaaaa=1, baabbb=1⟩φ(a) = bbbbbbbb, φ(b) = b
1113306⟨a, b | aaaaa=1, bbaabb=1⟩φ(a) = bbbbbbbb, φ(b) = b
1116606⟨a, b | aaaa=1, abbabbb=1⟩φ(a) = bbbbb, φ(b) = bbbbbbbbbbbbbbbbbb
1116608⟨a, b | aaaa=1, abbbabb=1⟩φ(a) = bbbbb, φ(b) = bbbbbbbbbbbbbbbbbb
1116623⟨a, b | aaaa=1, babbabb=1⟩φ(a) = bbbbb, φ(b) = bbbbbbbbbbbbbbbbbb
1116624⟨a, b | aaaa=1, babbbab=1⟩φ(a) = bbbbb, φ(b) = bbbbbbbbbbbbbbbbbb