#5088 ⟨a, b | aaa=bb, baab=a⟩

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Contents

  1. Properties
  2. Finite structure
  3. Right Cayley graph
  4. Left Cayley graph
  5. Rewriting system
  6. Same cardinality
  7. Isomorphic instances

Properties

Finite structure

Elements in the center commute with all other elements.
An idempotent element x satisfies x2 = x.
The index and period of x is the least m (index) and n (period) such that x(m+n) = xm.

Right Cayley graph

Left Cayley graph

Rewriting system

Format:
Word:
Enter a word above to compute its normal form. Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Strategy:
Result: 1 
1
#RuleProof
1. a13 ⇒ a [4]
2. ab ⇒ ba5 [3]
3. b2 ⇒ a3 [1]
# ab:aaa=bb,baab=a a/b - -
aaaaaaaaaaaaa=a
ab=baaaaa
bb=aaa

Same cardinality

5 unique, 25 total

Σ#PresentationPropertiesφ
93645⟨a, b | aa=1, abab=bbb⟩Noc 2619
107050⟨a, b | bb=aa, ababa=a⟩Noc 26
1115941⟨a, b | aba=bb, bbabb=a⟩Noc 26
1119766⟨a, b | aba=b, babbb=aa⟩Noc 26
1126639⟨a, b | aa=1, abbbbbbb=b⟩Noc 261

Isomorphic instances

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

1 total

Σ#PresentationMapping
107051⟨a, b | bb=aa, ababa=b⟩φ(a) = b, φ(b) = baa