#555 ⟨a, b | abbba=bab⟩

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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. ab ⇒ c [2]
2. cb ⇒ d [3]
3. db ⇒ e [4]
4. ea ⇒ bc [6]
5. ec ⇒ bd [7]
6. ed ⇒ be [8]
7. beb ⇒ e2 [9]
8. ceb ⇒ ae2 [10]
9. deb ⇒ ce2 [11]
10. e2b ⇒ de2 [12]
# ab:abbba=bab bacde ab=c,cb=d,db=e morph:2/1,2/1,2/0
ab=c
cb=d
db=e
ea=bc
ec=bd
ed=be
beb=ee
ceb=aee
deb=cee
eeb=dee

Other submonoids of same group

12 unique, 57 total

Σ#PresentationDescriptionRelated
530⟨a, b | aabba=1⟩Infinite non-Abelian group40 iso
543⟨a, b | abba=b⟩Infinite cancellative non-commutative monoid
546⟨a, b | aaa=bb⟩Infinite cancellative non-commutative monoid
553⟨a, b | aba=bb⟩Infinite cancellative non-commutative monoid
691⟨a, b | ababa=b⟩Infinite cancellative non-commutative monoid5 iso
6123⟨a, b | bab=aba⟩Infinite cancellative non-commutative monoid
7267⟨a, b | abba=bab⟩Infinite cancellative non-commutative monoid
91137⟨a, b | abbbba=bab⟩Infinite cancellative non-commutative monoid
91262⟨a, b | ababa=baab⟩Infinite cancellative non-commutative monoid
102361⟨a, b | abbbbba=bab⟩Infinite cancellative non-commutative monoid
114887⟨a, b | abbbbbba=bab⟩Infinite cancellative non-commutative monoid
115855⟨a, b | abaaba=baaab⟩Infinite cancellative non-commutative monoid