#2489 ⟨a, b | aabaab=baba⟩

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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. bac ⇒ cba [4]
2. a2bc ⇒ ca2b [5]
3. a2ba2c ⇒ caba [6]
4. (ba)2 ⇒ c [2]
5. (a2b)2 ⇒ c [3]
6. babc ⇒ caba2b [7]
# ab:aabaab=baba a/cb baba=c magic:0
bac=cba
aabc=caab
aabaac=caba
baba=c
aabaab=c
babc=cabaab

Other submonoids of same group

4 unique, 4 total

Σ#PresentationDescriptionRelated
8453⟨a, b | aababb=ba⟩Infinite cancellative non-commutative monoid
8527⟨a, b | aabab=bba⟩Infinite cancellative non-commutative monoid
101952⟨a, b | aabaabab=ba⟩Infinite cancellative non-commutative monoid
102309⟨a, b | abaabab=baa⟩Infinite cancellative non-commutative monoid