#1264 ⟨a, b | ababa=bbbb⟩

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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(ba)2 ⇒ b4 [1]
2. b5a ⇒ ab5 [2]
# ab:ababa=bbbb ab
ababa=bbbb
bbbbba=abbbbb

Other submonoids of same group

5 unique, 12 total

Σ#PresentationDescriptionRelated
8283⟨a, b | aaaabbba=1⟩Infinite non-Abelian group7 iso
8490⟨a, b | aaaaa=bbb⟩Infinite cancellative non-commutative monoid
102356⟨a, b | abbabba=bbb⟩Infinite cancellative non-commutative monoid
114301⟨a, b | ababababa=bb⟩Infinite cancellative non-commutative monoid
114357⟨a, b | abbbabbba=bb⟩Infinite cancellative non-commutative monoid