#1616 ⟨a, b | aaabaabaa=b⟩

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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. a3ba2b2 ⇒ ba(ba2)2 [2]
2. a(a2b)2ab ⇒ (ba2)3 [3]
3. a3(ba2)2 ⇒ b [1]
# ab:aaabaabaa=b ba
aaabaabb=babaabaa
aaabaabab=baabaabaa
aaabaabaa=b

Other submonoids of same group

6 unique, 11 total

Σ#PresentationDescriptionRelated
8431⟨a, b | aaabaa=bb⟩Infinite cancellative non-commutative monoid
91038⟨a, b | aaabaa=bab⟩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

3 unique, 3 total

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