#2443 ⟨a, b | aaa=1, abbbb=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. b10 ⇒ b
  2. ab ⇒ b7
  3. a3 ⇒ 1 
# ab:aaa=1,abbbb=b b/a
bbbbbbbbbb=b
ab=bbbbbbb
aaa=1

Right Cayley graph

Left Cayley graph

Others with same cardinality

8 unique, 104 total

Σ#PresentationDescriptionRelated
91470⟨a, b | aaa=bb, abab=1⟩Finite non-Abelian group with 30 elements73 iso
91907⟨a, b | aab=a, bbbbb=1⟩Finite non-commutative monoid with 30 elements11 iso, 4 anti-iso
106560⟨a, b | aaa=a, bbbb=ab⟩Finite non-commutative monoid with 30 elements
107013⟨a, b | ab=aa, bbbbb=b⟩Finite non-commutative monoid with 30 elements
1111058⟨a, b | abba=bbb, baba=1⟩Finite non-Abelian group with 30 elements8 iso
1113115⟨a, b | bbb=aaa, aaba=b⟩Finite non-commutative monoid with 30 elements
1115979⟨a, b | aaa=aa, bbbb=ab⟩Finite non-commutative monoid with 30 elements
1120847⟨a, b | ab=aa, bbbbb=bb⟩Finite non-commutative monoid with 30 elements

Other isomorphic instances

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

14 total

Σ#PresentationMapping
92594⟨a, b | aaa=1, bbbb=ab⟩φ(a) = a, φ(b) = bb
107509⟨a, b | aaa=1, aabbbb=b⟩φ(a) = a, φ(b) = bb
107521⟨a, b | aaa=1, ababbb=b⟩φ(a) = a, φ(b) = bb
107525⟨a, b | aaa=1, abbabb=b⟩φ(a) = a, φ(b) = bb
107527⟨a, b | aaa=1, abbbab=b⟩φ(a) = a, φ(b) = bb
108091⟨a, b | aaa=1, bbbb=aab⟩φ(a) = a, φ(b) = b
1122247⟨a, b | aaa=1, aabbbb=ab⟩φ(a) = a, φ(b) = b
1122304⟨a, b | aaa=1, baabbb=ab⟩φ(a) = a, φ(b) = b
1122308⟨a, b | aaa=1, bababb=ab⟩φ(a) = a, φ(b) = b
1122312⟨a, b | aaa=1, babbab=ab⟩φ(a) = a, φ(b) = b
1122319⟨a, b | aaa=1, bbaabb=ab⟩φ(a) = a, φ(b) = b
1122817⟨a, b | aaa=1, abbbb=aab⟩φ(a) = a, φ(b) = bb
1122845⟨a, b | aaa=1, babbb=aab⟩φ(a) = a, φ(b) = bb
1122853⟨a, b | aaa=1, bbabb=aab⟩φ(a) = a, φ(b) = bb

Other anti-isomorphic instances

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

5 total

Σ#PresentationMapping
1122286⟨a, b | aaa=1, abbbba=ab⟩φ(a) = a, φ(b) = b
1122305⟨a, b | aaa=1, baabbb=ba⟩φ(a) = a, φ(b) = b
1122309⟨a, b | aaa=1, bababb=ba⟩φ(a) = a, φ(b) = b
1122818⟨a, b | aaa=1, abbbb=aba⟩φ(a) = a, φ(b) = bb
1122848⟨a, b | aaa=1, babbb=baa⟩φ(a) = a, φ(b) = bb