#5942 ⟨a, b | abbbba=babbb⟩

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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. cba ⇒ bc [6]
2. cb3 ⇒ ab3c [5]
3. cab3 ⇒ bab2c [4]
4. bab3 ⇒ c [2]
5. ab4a ⇒ c [3]
# ab:abbbba=babbb ac/b babbb=c magic:0
cba=bc
cbbb=abbbc
cabbb=babbc
babbb=c
abbbba=c

Other submonoids of same group

6 unique, 24 total

Σ#PresentationDescriptionRelated
7207⟨a, b | aaaba=bb⟩Infinite cancellative non-commutative monoid
8504⟨a, b | aaaba=bab⟩Infinite cancellative non-commutative monoid
9670⟨a, b | aabababba=1⟩Infinite non-Abelian group8 iso, 10 anti-iso
9850⟨a, b | abababba=b⟩Infinite cancellative non-commutative monoid
91174⟨a, b | aaaba=baab⟩Infinite cancellative non-commutative monoid
114828⟨a, b | abababba=bab⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

6 unique, 6 total

Σ#PresentationDescriptionRelated
7174⟨a, b | aaabba=b⟩Infinite cancellative non-commutative monoid
8362⟨a, b | aaababa=b⟩Infinite cancellative non-commutative monoid
9765⟨a, b | aaabaaba=b⟩Infinite cancellative non-commutative monoid
101612⟨a, b | aaabaaaba=b⟩Infinite cancellative non-commutative monoid
102742⟨a, b | baaab=aaaba⟩Infinite cancellative non-commutative monoid
113430⟨a, b | aaabaaaaba=b⟩Infinite cancellative non-commutative monoid