#1137 ⟨a, b | abbbba=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. eb ⇒ f [5]
5. fa ⇒ bc [7]
6. fc ⇒ bd [8]
7. fd ⇒ be [9]
8. fe ⇒ bf [10]
9. bfb ⇒ f2 [11]
10. cfb ⇒ af2 [12]
11. dfb ⇒ cf2 [13]
12. efb ⇒ df2 [14]
13. f2b ⇒ ef2 [15]
# ab:abbbba=bab bacdef ab=c,cb=d,db=e,eb=f morph:2/1,2/1,2/1,2/0
ab=c
cb=d
db=e
eb=f
fa=bc
fc=bd
fd=be
fe=bf
bfb=ff
cfb=aff
dfb=cff
efb=dff
ffb=eff

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
8555⟨a, b | abbba=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