#3474 ⟨a, b, c | ba=ac, cbb=a⟩

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Contents

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Other submonoids of anti-isomorphic 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. ac ⇒ ba [1]
2. cb2 ⇒ a [2]
3. bab2 ⇒ a2 [3]
4. a2b2 ⇒ cba2 [4]
# abc:ba=ac,cbb=a bca - -
ac=ba
cbb=a
babb=aa
aabb=cbaa

Other submonoids of same group

4 unique, 9 total

Σ#PresentationPropertiesφ
82988⟨a, b, c | aab=c, bcb=a⟩Can Inf2
83510⟨a, b, c | bb=ac, aba=c⟩Can Inf2
85585⟨a, b, c | ab=c, bcac=a⟩Can Inf
86037⟨a, b, c | ab=c, aca=bc⟩Can Inf1

Other submonoids of anti-isomorphic group

5 unique, 50 total

Σ#PresentationPropertiesφ
81714⟨a, b, c | aab=bc, cba=1⟩Grp Inf38
82984⟨a, b, c | aab=c, bbc=a⟩Can Inf5
83524⟨a, b, c | bb=ac, baa=c⟩Can Inf2
83535⟨a, b, c | bb=ac, bca=c⟩Can Inf
85568⟨a, b, c | ab=c, bacc=a⟩Can Inf