#4509 ⟨a, b | aaba=b, bbbbb=1⟩

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Contents

  1. Properties
  2. Finite structure
  3. Right Cayley graph
  4. Left Cayley graph
  5. Rewriting system
  6. Isomorphic instances
  7. Anti-isomorphic instances

Properties

Finite structure

Elements in the center commute with all other elements.
The order of x is the least n such that xn = 1.

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. a33 ⇒ 1 [20]
2. ab ⇒ ba16 [19]
3. b5 ⇒ 1 [2]
# ab:aaba=b,bbbbb=1 a/b - -
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa=1
ab=baaaaaaaaaaaaaaaa
bbbbb=1

Isomorphic instances

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

6 total

Σ#PresentationMapping
1111445⟨a, b | aabba=b, bbbbb=1⟩φ(a) = bbbba, φ(b) = bbb
1111947⟨a, b | aaba=bb, bbbbb=1⟩φ(a) = ba, φ(b) = bbb
1113283⟨a, b | aaaaa=1, aababb=1⟩φ(a) = bbbb, φ(b) = ba
1113292⟨a, b | aaaaa=1, ababba=1⟩φ(a) = bbbb, φ(b) = ba
1113294⟨a, b | aaaaa=1, abbaab=1⟩φ(a) = bbbb, φ(b) = ba
1113301⟨a, b | aaaaa=1, baabab=1⟩φ(a) = bbbb, φ(b) = ba

Anti-isomorphic instances

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

2 total

Σ#PresentationMapping
1113285⟨a, b | aaaaa=1, aabbab=1⟩φ(a) = bbbb, φ(b) = ba
1113290⟨a, b | aaaaa=1, abaabb=1⟩φ(a) = bbbb, φ(b) = ba