#15526 ⟨a, b | aaa=bb, ababb=b⟩

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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. a18 ⇒ a3 [7]
2. ba15 ⇒ b [6]
3. ab ⇒ ba11 [5]
4. b2 ⇒ a3 [1]
# ab:aaa=bb,ababb=b a/b - -
aaaaaaaaaaaaaaaaaa=aaa
baaaaaaaaaaaaaaa=b
ab=baaaaaaaaaaa
bb=aaa

Same cardinality

1 unique, 1 total

Σ#PresentationProperties
1118737⟨a, b | aaa=a, abbbba=b⟩Noc 33

Isomorphic instances

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

1 total

Σ#PresentationMapping
1115530⟨a, b | aaa=bb, abbba=b⟩φ(a) = a, φ(b) = b