#11058 ⟨a, b | abba=bbb, baba=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. b15 ⇒ 1
  2. ba ⇒ ab4
  3. a2 ⇒ b10 
# ab:abba=bbb,baba=1 b/a
bbbbbbbbbbbbbbb=1
ba=abbbb
aa=bbbbbbbbbb

Right Cayley graph

Left Cayley graph

Others with same cardinality

8 unique, 115 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
92443⟨a, b | aaa=1, abbbb=b⟩Finite non-commutative monoid with 30 elements14 iso, 5 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
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.

8 total

Σ#PresentationMapping
1116958⟨a, b | abab=1, aaaabba=1⟩φ(a) = b, φ(b) = a
1116964⟨a, b | abab=1, aaabbaa=1⟩φ(a) = b, φ(b) = a
1116974⟨a, b | abab=1, aabbaaa=1⟩φ(a) = b, φ(b) = a
1116991⟨a, b | abab=1, abbaaaa=1⟩φ(a) = b, φ(b) = a
1116999⟨a, b | abab=1, abbbbba=1⟩φ(a) = a, φ(b) = b
1117012⟨a, b | abab=1, bbaaaaa=1⟩φ(a) = b, φ(b) = a
1118014⟨a, b | abab=1, aaaab=ba⟩φ(a) = b, φ(b) = a
1118057⟨a, b | abab=1, baaaa=ab⟩φ(a) = b, φ(b) = a