#3072 ⟨a, b, c | abc=b, cba=b⟩

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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. abc ⇒ b [1]
2. cba ⇒ b [2]
3. b2a ⇒ ab2 [3]
4. b2c ⇒ cb2 [4]
# abc:abc=b,cba=b acb - -
abc=b
cba=b
bba=abb
bbc=cbb

Other submonoids of same group

8 unique, 16 total

Σ#PresentationPropertiesφ
7533⟨a, b, c | ba=ab, cc=a⟩Can Inf
82199⟨a, b, c | aabc=1, acba=1⟩Grp Inf5
82976⟨a, b, c | aab=c, baa=c⟩Can Inf2
83431⟨a, b, c | ba=ab, cac=b⟩Can Inf
83587⟨a, b, c | ba=ab, cc=ab⟩Can Inf1
83592⟨a, b, c | ba=ac, ca=ab⟩Can Inf
83596⟨a, b, c | ba=ac, cc=bb⟩Can Inf
86088⟨a, b, c | ab=c, bca=cc⟩Can Inf