#6428 ⟨a, b | aab=b, babbb=a⟩

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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. ab8 ⇒ a
  3. ba ⇒ ab5
  4. a2 ⇒ b8 
# ab:aab=b,babbb=a b/a
bbbbbbbbb=b
abbbbbbbb=a
ba=abbbbb
aa=bbbbbbbb

Cayley table

Idempotents are shown in bold.

1ababb2ab2b3ab3b4ab4b5ab5b6ab6b7ab7b8
11ababb2ab2b3ab3b4ab4b5ab5b6ab6b7ab7b8
aab8abbab2b2ab3b3ab4b4ab5b5ab6b6ab7b7a
bbab5b2ab6b3ab7b4ab5abb6ab2b7ab3b8ab4b
ababb5ab2b6ab3b7ab4b8ab5bab6b2ab7b3ab4ab
b2b2ab2b3ab3b4ab4b5ab5b6ab6b7ab7b8ababb2
ab2ab2b2ab3b3ab4b4ab5b5ab6b6ab7b7ab8abbab2
b3b3ab7b4ab5abb6ab2b7ab3b8ab4bab5b2ab6b3
ab3ab3b7ab4b8ab5bab6b2ab7b3ab4abb5ab2b6ab3
b4b4ab4b5ab5b6ab6b7ab7b8ababb2ab2b3ab3b4
ab4ab4b4ab5b5ab6b6ab7b7ab8abbab2b2ab3b3ab4
b5b5abb6ab2b7ab3b8ab4bab5b2ab6b3ab7b4ab5
ab5ab5bab6b2ab7b3ab4abb5ab2b6ab3b7ab4b8ab5
b6b6ab6b7ab7b8ababb2ab2b3ab3b4ab4b5ab5b6
ab6ab6b6ab7b7ab8abbab2b2ab3b3ab4b4ab5b5ab6
b7b7ab3b8ab4bab5b2ab6b3ab7b4ab5abb6ab2b7
ab7ab7b3ab4abb5ab2b6ab3b7ab4b8ab5bab6b2ab7
b8b8ababb2ab2b3ab3b4ab4b5ab5b6ab6b7ab7b8

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

16 unique, 69 total

Σ#PresentationDescriptionRelated
104375⟨a, b | aaaa=b, abbbb=1⟩Isomorphic to ℤ1739 iso
106514⟨a, b | aba=b, baaab=a⟩Finite non-commutative monoid with 17 elements
107152⟨a, b | bb=aa, abab=aa⟩Finite non-commutative monoid with 17 elements
107153⟨a, b | bb=aa, abab=ab⟩Finite non-commutative monoid with 17 elements
107154⟨a, b | bb=aa, abab=ba⟩Finite non-commutative monoid with 17 elements
1113141⟨a, b | aab=aaa, bbb=ab⟩Finite non-commutative monoid with 17 elements
1113142⟨a, b | aab=aaa, bbb=ba⟩Finite non-commutative monoid with 17 elements
1113151⟨a, b | aba=aaa, baa=bb⟩Finite non-commutative monoid with 17 elements
1113156⟨a, b | aba=aaa, bbb=ab⟩Finite non-commutative monoid with 17 elements
1113218⟨a, b | abb=aba, bbb=aa⟩Finite non-commutative monoid with 17 elements
1114395⟨a, b | aaaa=b, abbbb=a⟩Isomorphic to ℕ(17 = 1)2 iso
1114396⟨a, b | aaaa=b, abbbb=b⟩Isomorphic to ℕ(17 = 4)2 iso
1114698⟨a, b | aabb=a, baaaa=b⟩Finite non-commutative monoid with 17 elements1 iso, 6 anti-iso
1115488⟨a, b | aaa=ab, babbb=b⟩Finite non-commutative monoid with 17 elements3 iso
1116143⟨a, b | aab=aa, bbbb=ba⟩Finite non-commutative monoid with 17 elements
1116521⟨a, b | aab=bb, bab=aaa⟩Finite non-commutative monoid with 17 elements

Other isomorphic instances

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

2 total

Σ#PresentationMapping
106440⟨a, b | aab=b, bbbab=a⟩φ(a) = a, φ(b) = b
106520⟨a, b | aba=b, babbb=a⟩φ(a) = abb, φ(b) = b