#2077 ⟨a, b | abbaabba=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. c2a ⇒ ac2 [5]
2. a(ca)2 ⇒ c [4]
3. c2b ⇒ acb(ac)2 [7]
4. (ac)2b ⇒ b(ac)2 [6]
5. b2 ⇒ (ac)2 [3]
# ab:abbaabba=bb ac/b bba=c morph:3/0
cca=acc
acaca=c
ccb=acbacac
acacb=bacac
bb=acac

Other submonoids of same group

1 unique, 5 total

Σ#PresentationDescriptionRelated
101370⟨a, b | aaabbaabba=1⟩Infinite non-Abelian group4 iso