#2767 ⟨a, b | babab=ababa⟩

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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. ca ⇒ bc [4]
2. cb ⇒ ac [5]
3. a(ba)2 ⇒ c [2]
4. b(ab)2 ⇒ c [3]
# ab:babab=ababa abc ababa=c magic:0
ca=bc
cb=ac
ababa=c
babab=c

Other submonoids of same group

7 unique, 18 total

Σ#PresentationDescriptionRelated
7131⟨a, b | aaaabba=1⟩Infinite non-Abelian group11 iso
7196⟨a, b | abbbba=b⟩Infinite cancellative non-commutative monoid
7199⟨a, b | aaaaa=bb⟩Infinite cancellative non-commutative monoid
7232⟨a, b | abbba=bb⟩Infinite cancellative non-commutative monoid
7237⟨a, b | aaaa=bab⟩Infinite cancellative non-commutative monoid
7268⟨a, b | abba=bbb⟩Infinite cancellative non-commutative monoid
102333⟨a, b | abababa=bab⟩Infinite cancellative non-commutative monoid