#1038 ⟨a, b | aaabaa=bab⟩

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Quick links

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Other submonoids of anti-isomorphic 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. a3ba2 ⇒ bab [1]
2. a3b2ab ⇒ (ba)3a [2]
3. a2(ab)3 ⇒ ba(ba2)2 [3]
# ab:aaabaa=bab ba
aaabaa=bab
aaabbab=bababaa
aaababab=babaabaa

Other submonoids of same group

5 unique, 10 total

Σ#PresentationDescriptionRelated
8431⟨a, b | aaabaa=bb⟩Infinite cancellative non-commutative monoid
102430⟨a, b | aaabaa=baab⟩Infinite cancellative non-commutative monoid
113070⟨a, b | aabababbaba=1⟩Infinite non-Abelian group1 iso, 4 anti-iso
113775⟨a, b | abababbaba=b⟩Infinite cancellative non-commutative monoid
115550⟨a, b | aaabaa=baaab⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

4 unique, 4 total

Σ#PresentationDescriptionRelated
8366⟨a, b | aaabbaa=b⟩Infinite cancellative non-commutative monoid
9769⟨a, b | aaababaa=b⟩Infinite cancellative non-commutative monoid
101616⟨a, b | aaabaabaa=b⟩Infinite cancellative non-commutative monoid
113434⟨a, b | aaabaaabaa=b⟩Infinite cancellative non-commutative monoid