#2450 ⟨a, b | aaa=1, babbb=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
  8. 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. b28 ⇒ 1 [11]
2. ab ⇒ b9a [9]
3. a3 ⇒ 1 [1]
# ab:aaa=1,babbb=a reversed:b/a - -
bbbbbbbbbbbbbbbbbbbbbbbbbbbb=1
ab=bbbbbbbbba
aaa=1

Same cardinality

1 unique, 8 total

Σ#PresentationPropertiesφ
107815⟨a, b | aaa=1, babbb=ab⟩Noc 847

Isomorphic instances

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

13 total

Σ#PresentationMapping
107230⟨a, b | aaa=1, aababbb=1⟩φ(a) = a, φ(b) = b
107248⟨a, b | aaa=1, ababbba=1⟩φ(a) = a, φ(b) = b
107255⟨a, b | aaa=1, abbbaab=1⟩φ(a) = a, φ(b) = b
107265⟨a, b | aaa=1, baababb=1⟩φ(a) = a, φ(b) = b
107540⟨a, b | aaa=1, bababb=a⟩φ(a) = a, φ(b) = baa
1121160⟨a, b | aaa=1, aabababb=1⟩φ(a) = a, φ(b) = baa
1121193⟨a, b | aaa=1, abababba=1⟩φ(a) = a, φ(b) = baa
1121195⟨a, b | aaa=1, ababbaab=1⟩φ(a) = a, φ(b) = baa
1121203⟨a, b | aaa=1, abbaabab=1⟩φ(a) = a, φ(b) = baa
1121229⟨a, b | aaa=1, baababab=1⟩φ(a) = a, φ(b) = baa
1121762⟨a, b | aaa=1, baababb=a⟩φ(a) = a, φ(b) = ba
1121764⟨a, b | aaa=1, baabbab=a⟩φ(a) = aa, φ(b) = baa
1122269⟨a, b | aaa=1, ababbb=aa⟩φ(a) = a, φ(b) = b

Anti-isomorphic instances

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

8 total

Σ#PresentationMapping
107235⟨a, b | aaa=1, aabbbab=1⟩φ(a) = a, φ(b) = b
107243⟨a, b | aaa=1, abaabbb=1⟩φ(a) = a, φ(b) = b
107268⟨a, b | aaa=1, babaabb=1⟩φ(a) = a, φ(b) = b
1121168⟨a, b | aaa=1, aabbabab=1⟩φ(a) = a, φ(b) = baa
1121187⟨a, b | aaa=1, abaabbab=1⟩φ(a) = a, φ(b) = baa
1121191⟨a, b | aaa=1, ababaabb=1⟩φ(a) = a, φ(b) = baa
1122281⟨a, b | aaa=1, abbbab=aa⟩φ(a) = a, φ(b) = b
1122303⟨a, b | aaa=1, baabbb=aa⟩φ(a) = a, φ(b) = b