#2 ⟨a, b, c | ab=1, ac=1⟩

Up:Monoid enumeration
Prev:#1 ⟨a, b, c | aa=1, bc=1⟩
Next:#3 ⟨a, b, c | ab=1, bc=1⟩

Contents

  1. Properties
  2. Rewriting system
  3. Isomorphic instances

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. ab ⇒ 1 [1]
2. ac ⇒ 1 [2]
# abc:ab=1,ac=1 abc - -
ab=1
ac=1

Isomorphic instances

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

36 total

Σ#PresentationMapping
6177⟨a, b, c | ab=1, aabc=1⟩φ(a) = a, φ(b) = b, φ(c) = c
6181⟨a, b, c | ab=1, abac=1⟩φ(a) = a, φ(b) = b, φ(c) = c
6236⟨a, b, c | ab=1, aca=a⟩φ(a) = a, φ(b) = b, φ(c) = c
6246⟨a, b, c | ab=1, bac=b⟩φ(a) = a, φ(b) = b, φ(c) = c
6262⟨a, b, c | ab=1, ac=ab⟩φ(a) = a, φ(b) = b, φ(c) = c
82560⟨a, b, c | aba=a, aabc=1⟩φ(a) = a, φ(b) = b, φ(c) = c
82564⟨a, b, c | aba=a, abac=1⟩φ(a) = a, φ(b) = b, φ(c) = c
82569⟨a, b, c | aba=a, acab=1⟩φ(a) = a, φ(b) = b, φ(c) = c
82577⟨a, b, c | aba=a, babc=1⟩φ(a) = b, φ(b) = a, φ(c) = c
82706⟨a, b, c | abc=a, babc=1⟩φ(a) = b, φ(b) = a, φ(c) = c
82716⟨a, b, c | abc=a, bbca=1⟩φ(a) = b, φ(b) = a, φ(c) = c
82722⟨a, b, c | abc=a, bcba=1⟩φ(a) = b, φ(b) = a, φ(c) = c
86279⟨a, b, c | ab=1, aaabbc=1⟩φ(a) = a, φ(b) = b, φ(c) = c
86293⟨a, b, c | ab=1, aababc=1⟩φ(a) = a, φ(b) = b, φ(c) = c
86297⟨a, b, c | ab=1, aabbac=1⟩φ(a) = a, φ(b) = b, φ(c) = c
86303⟨a, b, c | ab=1, aabcab=1⟩φ(a) = a, φ(b) = b, φ(c) = c
86337⟨a, b, c | ab=1, abaabc=1⟩φ(a) = a, φ(b) = b, φ(c) = c
86341⟨a, b, c | ab=1, ababac=1⟩φ(a) = a, φ(b) = b, φ(c) = c
86347⟨a, b, c | ab=1, abacab=1⟩φ(a) = a, φ(b) = b, φ(c) = c
86808⟨a, b, c | ab=1, aabca=a⟩φ(a) = a, φ(b) = b, φ(c) = c
86852⟨a, b, c | ab=1, abaca=a⟩φ(a) = a, φ(b) = b, φ(c) = c
86863⟨a, b, c | ab=1, abbac=b⟩φ(a) = a, φ(b) = b, φ(c) = c
86907⟨a, b, c | ab=1, acaba=a⟩φ(a) = a, φ(b) = b, φ(c) = c
86966⟨a, b, c | ab=1, baabc=b⟩φ(a) = a, φ(b) = b, φ(c) = c
86976⟨a, b, c | ab=1, babac=b⟩φ(a) = a, φ(b) = b, φ(c) = c
87301⟨a, b, c | ab=1, aabb=ac⟩φ(a) = a, φ(b) = b, φ(c) = c
87305⟨a, b, c | ab=1, aabc=ab⟩φ(a) = a, φ(b) = b, φ(c) = c
87345⟨a, b, c | ab=1, abab=ac⟩φ(a) = a, φ(b) = b, φ(c) = c
87349⟨a, b, c | ab=1, abac=ab⟩φ(a) = a, φ(b) = b, φ(c) = c
87398⟨a, b, c | ab=1, acaa=aa⟩φ(a) = a, φ(b) = b, φ(c) = c
87487⟨a, b, c | ab=1, baca=ba⟩φ(a) = a, φ(b) = b, φ(c) = c
87509⟨a, b, c | ab=1, bbac=bb⟩φ(a) = a, φ(b) = b, φ(c) = c
87717⟨a, b, c | ab=1, aca=aab⟩φ(a) = a, φ(b) = b, φ(c) = c
87719⟨a, b, c | ab=1, aca=aba⟩φ(a) = a, φ(b) = b, φ(c) = c
87749⟨a, b, c | ab=1, bac=abb⟩φ(a) = a, φ(b) = b, φ(c) = c
87755⟨a, b, c | ab=1, bac=bab⟩φ(a) = a, φ(b) = b, φ(c) = c