#869 ⟨a, b | aaaaaaa=bb⟩

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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. b2a ⇒ ab2 [2]
2. a7 ⇒ b2 [1]
# ab:aaaaaaa=bb ab
bba=abb
aaaaaaa=bb

Other submonoids of same group

7 unique, 15 total

Σ#PresentationDescriptionRelated
9601⟨a, b | aaaaaabba=1⟩Infinite non-Abelian group8 iso
9866⟨a, b | abbbbbba=b⟩Infinite cancellative non-commutative monoid
91002⟨a, b | abbbbba=bb⟩Infinite cancellative non-commutative monoid
91007⟨a, b | aaaaaa=bab⟩Infinite cancellative non-commutative monoid
91138⟨a, b | abbbba=bbb⟩Infinite cancellative non-commutative monoid
91146⟨a, b | aaaaa=baab⟩Infinite cancellative non-commutative monoid
91274⟨a, b | abbba=bbbb⟩Infinite cancellative non-commutative monoid