#6101 ⟨a, b, c | ab=c, cac=ba⟩

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Contents

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group

Properties

Rewriting system

Format:
Word:
Enter a word above to compute its normal form. Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Strategy:
Result: 1 
1
#RuleProof
1. bd ⇒ d4b [12]
2. cd ⇒ d2c [10]
3. ad2 ⇒ da [8]
4. ab ⇒ c [1]
5. bc ⇒ d2cb [11]
6. c2 ⇒ d2b [9]
7. ac ⇒ d [3]
8. ba ⇒ d2c [13]
9. ca ⇒ d2 [5]
# abc:ab=c,cac=ba reversed:d/bca ac=d morph:2/0
bd=ddddb
cd=ddc
add=da
ab=c
bc=ddcb
cc=ddb
ac=d
ba=ddc
ca=dd

Other submonoids of same group

6 unique, 26 total

Σ#PresentationPropertiesφ
7417⟨a, b, c | abc=b, cba=1⟩Grp Inf10
7537⟨a, b, c | ba=ac, bb=c⟩Can Inf4
7554⟨a, b, c | bb=ac, ca=b⟩Can Inf3
71041⟨a, b, c | ab=c, bca=c⟩Can Inf2
85567⟨a, b, c | ab=c, baca=c⟩Can Inf
85675⟨a, b, c | aa=b, aac=ca⟩Can Inf1