#2236 ⟨a, b | aababaa=bbb⟩

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Quick links

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group

Properties

Rewriting system

Format:
Word to reduce:
Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Reduction strategy:
Path to normal form: 1 
1
#RuleProof
1. a(ab)2a2 ⇒ b3 [1]
2. b4aba2 ⇒ a2bab4 [2]
3. b2(ba)3a ⇒ a(ab)3b2 [3]
# ab:aababaa=bbb ab
aababaa=bbb
bbbbabaa=aababbbb
bbbababaa=aabababbb

Other submonoids of same group

2 unique, 5 total

Σ#PresentationDescriptionRelated
112949⟨a, b | aaababbbaba=1⟩Infinite non-Abelian group3 iso
114122⟨a, b | aabababaa=bb⟩Infinite cancellative non-commutative monoid