#2361 ⟨a, b | abbbbba=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. fb ⇒ g [6]
6. ga ⇒ bc [8]
7. gc ⇒ bd [9]
8. gd ⇒ be [10]
9. ge ⇒ bf [11]
10. gf ⇒ bg [12]
11. bgb ⇒ g2 [13]
12. cgb ⇒ ag2 [14]
13. dgb ⇒ cg2 [15]
14. egb ⇒ dg2 [16]
15. fgb ⇒ eg2 [17]
16. g2b ⇒ fg2 [18]
# ab:abbbbba=bab bacdefg ab=c,cb=d,db=e,eb=f,fb=g morph:2/1,2/1,2/1,2/1,2/0
ab=c
cb=d
db=e
eb=f
fb=g
ga=bc
gc=bd
gd=be
ge=bf
gf=bg
bgb=gg
cgb=agg
dgb=cgg
egb=dgg
fgb=egg
ggb=fgg

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
91137⟨a, b | abbbba=bab⟩Infinite cancellative non-commutative monoid
91262⟨a, b | ababa=baab⟩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