#5943 ⟨a, b | abbbba=bbabb⟩

Up:Monoids with two generators and one relation
Prev:#5942 ⟨a, b | abbbba=babbb⟩
Next:#5944 ⟨a, b | abbbba=bbbbb⟩

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. ac ⇒ d [3]
2. bc ⇒ cb [7]
3. b2 ⇒ c [2]
4. dc ⇒ e [4]
5. ea ⇒ cd [6]
6. ed ⇒ ce [8]
7. cec ⇒ e2 [9]
8. dec ⇒ ae2 [10]
9. e2c ⇒ de2 [11]
10. cbec ⇒ be2 [12]
11. dbec ⇒ abe2 [13]
12. ebec ⇒ dbe2 [14]
# ab:abbbba=bbabb acbde bb=c,ac=d,dc=e morph:2/0,2/1,2/0
ac=d
bc=cb
bb=c
dc=e
ea=cd
ed=ce
cec=ee
dec=aee
eec=dee
cbec=bee
dbec=abee
ebec=dbee

Other submonoids of same group

11 unique, 23 total

Σ#PresentationDescriptionRelated
7182⟨a, b | aabbaa=b⟩Infinite cancellative non-commutative monoid1 iso
7214⟨a, b | aabaa=bb⟩Infinite cancellative non-commutative monoid
8378⟨a, b | aababaa=b⟩Infinite cancellative non-commutative monoid
8519⟨a, b | aabaa=bab⟩Infinite cancellative non-commutative monoid
9672⟨a, b | aababbaba=1⟩Infinite non-Abelian group10 iso
9796⟨a, b | aabaabaa=b⟩Infinite cancellative non-commutative monoid
9854⟨a, b | ababbaba=b⟩Infinite cancellative non-commutative monoid1 iso
91204⟨a, b | aabaa=baab⟩Infinite cancellative non-commutative monoid
101670⟨a, b | aabaaabaa=b⟩Infinite cancellative non-commutative monoid
102743⟨a, b | baaab=aabaa⟩Infinite cancellative non-commutative monoid
114843⟨a, b | ababbaba=bab⟩Infinite cancellative non-commutative monoid