#21778 ⟨a, b | aaa=1, babbbbb=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

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. b126 ⇒ 1 [82]
2. ab ⇒ b25a [83]
3. a3 ⇒ 1 [1]
# ab:aaa=1,babbbbb=a reversed:b/a - -
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=1
ab=bbbbbbbbbbbbbbbbbbbbbbbbba
aaa=1

Same cardinality

1 unique, 1 total

Σ#PresentationProperties
1114128⟨a, b | aaba=b, bbbbbb=1⟩Grp 378