#14698 ⟨a, b | aabb=a, baaaa=b⟩

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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 ⇒ b7
  4. a2 ⇒ ab6 
# ab:aabb=a,baaaa=b b/a
bbbbbbbbb=b
abbbbbbbb=a
ba=bbbbbbb
aa=abbbbbb

Cayley table

Idempotents are shown in bold.

1ababb2ab2b3ab3b4ab4b5ab5b6ab6b7ab7b8
11ababb2ab2b3ab3b4ab4b5ab5b6ab6b7ab7b8
aaab6abab7ab2aab3abab4ab2ab5ab3ab6ab4ab7ab5a
bbb7b2b8b3bb4b2b5b3b6b4b7b5b8b6b
ababab7ab2aab3abab4ab2ab5ab3ab6ab4ab7ab5aab6ab
b2b2b8b3bb4b2b5b3b6b4b7b5b8b6bb7b2
ab2ab2aab3abab4ab2ab5ab3ab6ab4ab7ab5aab6abab7ab2
b3b3bb4b2b5b3b6b4b7b5b8b6bb7b2b8b3
ab3ab3abab4ab2ab5ab3ab6ab4ab7ab5aab6abab7ab2aab3
b4b4b2b5b3b6b4b7b5b8b6bb7b2b8b3bb4
ab4ab4ab2ab5ab3ab6ab4ab7ab5aab6abab7ab2aab3abab4
b5b5b3b6b4b7b5b8b6bb7b2b8b3bb4b2b5
ab5ab5ab3ab6ab4ab7ab5aab6abab7ab2aab3abab4ab2ab5
b6b6b4b7b5b8b6bb7b2b8b3bb4b2b5b3b6
ab6ab6ab4ab7ab5aab6abab7ab2aab3abab4ab2ab5ab3ab6
b7b7b5b8b6bb7b2b8b3bb4b2b5b3b6b4b7
ab7ab7ab5aab6abab7ab2aab3abab4ab2ab5ab3ab6ab4ab7
b8b8b6bb7b2b8b3bb4b2b5b3b6b4b7b5b8

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

16 unique, 64 total

Σ#PresentationDescriptionRelated
104375⟨a, b | aaaa=b, abbbb=1⟩Isomorphic to ℤ1739 iso
106428⟨a, b | aab=b, babbb=a⟩Finite non-commutative monoid with 17 elements2 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
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.

1 total

Σ#PresentationMapping
1114762⟨a, b | abab=a, baaaa=b⟩φ(a) = a, φ(b) = b

Other anti-isomorphic instances

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

6 total

Σ#PresentationMapping
1114796⟨a, b | abba=a, aaaab=b⟩φ(a) = a, φ(b) = b
1119020⟨a, b | aab=b, abbbba=a⟩φ(a) = bbbb, φ(b) = ab
1119052⟨a, b | aab=b, babbba=a⟩φ(a) = bbbb, φ(b) = ab
1119068⟨a, b | aab=b, bbabba=a⟩φ(a) = bbbb, φ(b) = ab
1119076⟨a, b | aab=b, bbbaba=a⟩φ(a) = bbbb, φ(b) = ab
1119080⟨a, b | aab=b, bbbbaa=a⟩φ(a) = bbbb, φ(b) = ab