#3594 ⟨a, b, c | ba=ac, cb=aa⟩

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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. ba ⇒ ac [1]
2. cb ⇒ a2 [2]
3. cac ⇒ a3 [3]
4. ca3 ⇒ a3b [4]
# abc:ba=ac,cb=aa abc - -
ba=ac
cb=aa
cac=aaa
caaa=aaab

Other submonoids of same group

10 unique, 117 total

Σ#PresentationPropertiesφ
7366⟨a, b, c | aba=b, cbc=1⟩Grp Inf93
7548⟨a, b, c | bb=aa, cc=a⟩Can Inf1
7938⟨a, b, c | aa=b, cbc=b⟩Can Inf5
82849⟨a, b, c | aaa=b, cac=b⟩Can Inf2
82851⟨a, b, c | aaa=b, cbc=a⟩Can Inf3
83041⟨a, b, c | aba=b, cac=b⟩Can Inf
83042⟨a, b, c | aba=b, cbc=a⟩Can Inf1
83472⟨a, b, c | ba=ac, cab=a⟩Can Inf
83501⟨a, b, c | bb=ac, aaa=c⟩Can Inf2
86095⟨a, b, c | ab=c, bcc=ca⟩Can Inf