#2504 ⟨a, b | aababa=baab⟩

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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. bc ⇒ caba [6]
2. ba2c ⇒ ca2b [4]
3. a2bac ⇒ cab [5]
4. ba2b ⇒ c [2]
5. a2(ba)2 ⇒ c [3]
# ab:aababa=baab a/cb baab=c magic:0
bc=caba
baac=caab
aabac=cab
baab=c
aababa=c

Other submonoids of same group

5 unique, 10 total

Σ#PresentationDescriptionRelated
8400⟨a, b | abaabba=b⟩Infinite cancellative non-commutative monoid
8534⟨a, b | aabba=bab⟩Infinite cancellative non-commutative monoid
101419⟨a, b | aababaabba=1⟩Infinite non-Abelian group5 iso
101758⟨a, b | abaaababa=b⟩Infinite cancellative non-commutative monoid
102340⟨a, b | ababbba=bab⟩Infinite cancellative non-commutative monoid